ProfOptimization2016

Publications

Preprints

  1. L. F. Prudente and D. R. Souza, Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems, submitted, 2023. [Codes]
  2. Gonçalves, M. L. N. Subsampled cubic regularization method for finite-sum minimization, 2022.
  3. Melo, J. G.; Monteiro, R. D. C.. Iteration-Complexity of a Linearized Proximal Multiblock ADMM Class for Linearly Constrained Nonconvex Optimization Problems, (Technical Report-2017).
  4. Melo, J. G.; Monteiro, R. D. C.. Iteration-Complexity of a Jacobi-type non-Euclidean ADMM for multi-block linearly constrained nonconvex programs (Technical Report-2017: PDF).

 Publications 2023

  1. Adona, V.A.; Gonçalves, M. L. N. An inexact version of the symmetric proximal ADMM for solving separable convex optimization.  Numerical Algorithms, 94, 1--28, 2023. (pdf)
  2. AGUIAR, A. A. ; FERREIRA, O. P. ; PRUDENTE, L. F. . Inexact gradient projection method with relative error tolerance. Computational Optimization and Applications 84, pp. 363–395 (2023).
  3. Assunção P. B.,  Ferreira O.P., and Prudente, L.F.: A generalized conditional gradient method for multiobjective composite optimization problems, Optimization, pp. 1-31, 2023. [PDF - Codes]
  4. Bello-Cruz, Y., Gonçalves, M. L. N., Krislock, N.. On FISTA with a relative error condition.  Computational Optimization and Applications, 84, 295-318, 2023.
  5. DA SILVA JUNIOR, P. C., FERREIRA, O. P., SECCHIN, L. D., SILVA, G. S.; Secant-inexact projection algorithms for solving a new class of constrained mixed generalized equations problems, J. Comput. Appl. Math., v. 440,  Paper No. 115638, 2023.
  6. DÍAZ MILLÁN, R., FERREIRA, O. P.; UGON,  J.; Approximate Douglas-Rachford algorithm for two-sets convex feasible problems, J. Global Optim, v. 86, p. 621-636, 2023 (pdf).
  7. FERREIRA, O. P.; NÉMETH, S. Z; ZHOU, JINZHEN. Convexity of sets and quadratic functions on the hyperbolic space,  J. Optim. Theory Appl., to appear 2023 (pdf).
  8. FERREIRA, O. P.; NÉMETH, S. Z; GAO, Y. Reducing the projection onto the monotone extended second-order cone to the pool-adjacent-violators algorithm of isotonic regression, Optimization, to appear 2023 (pdf).
  9. FERREIRA, O. P.; NÉMETH, S. Z; ZHOU, JINZHEN. Convexity of Non-homogeneous Quadratic Functions on the Hyperbolic Space,  J. Optim. Theory Appl.,v 199, p.1085-1105,2023 (pdf).
  10. FERREIRA, O. P.; GRAPIGLIA,G. N.; SANTOS, E. M.; SOUZA, J. C. O; .A subgradient method with non-monotone line search, Comput. Optim. and Appl., v. 84, n. 1,  p. 397-420, 2023 (pdf).

  11. FERREIRA, O. P.;  JEAN-ALEXIS, CÉLIA; PIÉTRUS, ALAIN; SILVA, G. N.  On Newton’s method for solving generalized equations, J. Complexity, v. 74, Paper No.101697, 17 pp,  2023 (pdf).

  12. Gonçalves, M. L. N.; Menezes, T.C. A framework for convex-constrained monotone nonlinear equations and its special cases. Computational and Applied Mathematics, 2023   (pdf)  [code] 
  13. Kong, Weiwei, Melo, J. G.; Monteiro, R. D. C.Iteration Complexity of an Inner Accelerated Inexact Proximal Augmented Lagrangian Method Based on the Classical Lagrangian Function. Siam Journal on Optimization, v. 33, p. 181-210, 2023.
  14.   Kong, Weiwei, Melo, J. G.; Monteiro, R. D. C.:  Iteration Complexity of a Proximal Augmented Lagrangian Method for Solving Nonconvex Composite Optimization Problems with Nonlinear Convex Constraints. Mathematics of Operations Research, v. 48, p. 1066-1094, 2023.
  15.  Kong, Weiwei, Melo, J. G.; Monteiro, R. D. C: A Proximal Augmented Lagrangian Method for Linearly Constrained Nonconvex Composite Optimization Problems. Journal of Optimization Theory and Applications,  2023.

Publications 2022

  1. O. P. Ferreira, M. V. Lemes, and L. F. Prudente, On the inexact scaled gradient projection method, Computational Optimization and Applications 81(1), pp. 91-125, 2022.
  2. M. L. N. Gonçalves, F. S. Lima, and L. F. Prudente, A study of Liu-Storey conjugate gradient methods for vector optimization, Applied Mathematics and Computation 425, pp. 127099, 2022. 
  3. Gonçalves, D. S., Gonçalves, M. L. N.; Menezes, T.C.. Inexact variable metric method for convex-constrained optimization problems.  Optimization, 71(1), 145-163, 2022.
  4. Grapiglia, G.N.; Gonçalves, M. L. N.; Silva, G.N. A Cubic Regularization of  Newton's Method with Finite-Difference Hessian Approximations.  Numerical Algorithms, 90, 607–630 (2022).
  5. FERREIRA, O. P.; SOSA, W. S.. On the Frank–Wolfe algorithm for non-compact constrained optimization problems, Optimization,v.71, n.1, p. 197-211, 2022.
  6. BORTOLOTI, M. A.de A.; FERNANDES, T. A. ; FERREIRA, O. P.. An efficient damped Newton-type algorithm with globalization strategy on Riemannian manifolds, J. Comput. Appl. Math., v. 403, Paper No. 113853, 15 pp,  2022.
  7. Yunier Bello-Cruz, Jefferson G. Melo & Ray V.G. Serra (2022) A proximal gradient splitting method for solving convex vector optimization problems, Optimization, 71:1, 33-53
  8. L. F. Prudente and D. R. Souza, A quasi-Newton method with Wolfe line searches for multiobjective optimization, Journal of Optimization Theory and Applications 194, pp. 1107-1140, 2022.
  9. G. C. Bento; CRUZ NETO, J. X. ; MEIRELES, L. V. ; SOUBEYRAN, A. .Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm. ANNALS OF OPERATIONS RESEARCH 316, pp. 1425–1443, 2022.
  10. Bento, G.C.; CRUZ NETO, J. X. ; MELO, I. D. L. . Combinatorial Convexity in Hadamard Manifolds: Existence for Equilibrium Problems. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, pp. 1087-1105, 2022.
  11. Bento, G.C.; CRUZ NETO, J. X. ; SOARES JUNIOR, P. A. ; SOUBEYRAN, A. . A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires. ANNALS OF OPERATIONS RESEARCH 316, pp. 1301–1318 (2022).
  12. GONÇALVES, MAX L. N. ; Melo, Jefferson G. ; MONTEIRO, RENATO D. C. . Projection-free accelerated method for convex optimization. OPTIMIZATION METHODS & SOFTWARE 37, pp. 214-240, 2022.
  13. AGUIAR, A. A. ; FERREIRA, O. P. ; PRUDENTE, L. F. . Subgradient method with feasible inexact projections for constrained convex optimization problems. OPTIMIZATION, v. 71, p. 3515-3537, 2022.
  14. GONÇALVES, M. L. N. ; LIMA, F. S. ; PRUDENTE, L. F. . Globally convergent Newton-type methods for multiobjective optimization. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 83, p. 403-434, 2022.

Publications 2021

  1. Iusem, A.N., Melo, J.G. & Serra, R.G. A Strongly Convergent Proximal Point Method for Vector Optimization. J Optim Theory Appl 190,183–200 (2021).
  2. Assunção, P. B., Ferreira, O. P.; Prudente, L. F.. Conditional gradient method for multiobjective optimization,  Computational Optimization and Applications,   v. 78, n. 3,  p. 741-768, 2021.
  3. R. Díaz Millán, O. P. Ferreira, and L. F. Prudente, Alternating conditional gradient method for convex feasibility problems, Computational Optimization and Applications 80(1), pp. 245-269, 2021.
  4. Gonçalves, D. S., Gonçalves, M. L. N.; Oliveira, F.R.. An inexact projected LM type algorithm for constrained nonlinear systems. Journal of Computational and Applied Mathematics, 391, 113-421, 2021.

Publications 2020

1. Adona, V.A.; Gonçalves, M. L. N.; Melo, J. G. An inexact proximal generalized alternating direction method of multipliers. Computational Optimization and Applications, 76(3), 621-647, 2020.

2. Batista, E. E. A; Bento, G. C; Ferreira, O. P. An extragradient-type algorithm for variational inequality on Hadamard manifolds. ESAIM: Control, Optimisation and Calculus of Variations, v. 26, Article Number 63, Number of page(s) 16, 2020.

3. Bento, G.C.,  Bitar, S.D. B. ; Da Cruz Neto, J. X.  ;  Soubeyran,, A.;  Souza, J. C.. A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems. Computational Optimization and Applications, 2020.

4. Bortoloti, M, A. De A. ; Fernandes, T. A. ; Ferreira, O. P. ; Yuan, JinYun. Damped Newton's method on Riemannian manifolds. Journal of Optimization Theory and Applications, v. 77, p. 643-660, 2020.

5. De Oliveira, F. R.; Ferreira, O. P.  Newton Method for Finding a Singularity of a Special Class of Locally Lipschitz Continuous Vector Fields on Riemannian Manifolds. Journal of Optimization Theory and Applications, v. 185, p. 522-539, 2020.

6. De Oliveira F. R.; Ferreira, O. P. Inexact Newton method with feasible inexact projections for solving constrained smooth and nonsmooth equations. Applied Numerical mathematics, v. 156, p. 63-76, 2020.

7. Ferreira, O. P; Louzeiro, M. S.; Prudente, L. F.. Iteration-complexity and asymptotic analysis of steepest descent method for multiobjective optimization on Riemannian manifolds.  Journal of Optimization Theory and Applications,  184, pp. 507-533, 2020.

8. Ferreira, O. P; Németh, S. Z.; Xiao, L. On the Spherical Quasi-convexity of Quadratic Functions on Spherically Subdual Convex Sets. Journal of Optimization Theory and Applications, v. 187, p. 1-21, 2020.

9. Ferreira, O.P.; Louzeiro, M. S.; Prudente, L. F. First Order Methods for Optimization on Riemannian Manifolds, Handbook of Variational Methods for Nonlinear Geometric Data, p. 499-525, 2020.

10. Gonçalves, M. L. N.; Prudente, L.F., On the extension of the Hager-Zhang conjugate gradient method for vector optimization. Computational Optimization and Applications, v. 76(3), p. 899-916, 2020.

11. Gonçalves, M. L. N.; Oliveira, F.R. On the global convergent of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems. Numerical Algorithms, 84(2), 609-631, 2020.

12. Gonçalves, M. L. N.; Menezes, T.C. Gauss-Newton method with approximate projections for solving constrained nonlinear least squares problems. Journal of Complexity, 58(1), 101459, 2020.

13. Gonçalves, M. L. N.; Melo, J. G.; Monteiro, R. D. C.. On the iteration-complexity of a non-Euclidean hybrid proximal extragradient and a proximal ADMM. Optimization, 69(4), 847-873, 2020.

14. Kong, W.; Melo, J. G.; Monteiro, R. D. C. . An efficient adaptive accelerated inexact proximal point method for solving linearly constrained nonconvex composite problems. Computational Optimization and Applications, v. 76, p. 305-346, 2020.

15. Marques-Alves, M.; Eckstein, J.; Geremia, M. ; Melo, J. G. . Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms. Computational Optimization and Applications, v. 75, p. 389-422, 2020.

 Publications 2019

1. Ferreira, O. P; Louzeiro, M. S.; Prudente, L. F..Gradient Method for Optimization on Riemannian Manifolds with Lower Bounded Curvature, SIAM J. Optim.,  29(4), p. 2517–2541, 2019, [MatLab_Codes]

2. Kong, W. ; Melo, Jefferson G. ; Monteiro, R. D. C. . Complexity of a Quadratic Penalty Accelerated Inexact Proximal Point Method for Solving Linearly Constrained Nonconvex Composite Programs. SIAM J. Optim.,, v. 29(4), p. 2566-2593, 2019.

3. Lucambio Pérez, L. R. and Prudente, L. F,  A Wolfe line search algorithm for vector optimization, ACM Transactions on Mathematical Software 45(4), pp. 37:1-37:23, 2019.

4. Díaz Millán, R., Machado, M. Pentón . Inexact proximal $$epsilon $$ -subgradient methods for composite convex optimization problems. Journal of Global Optimization, v. 75 (4), p. 1029–1060, 2019.

5. Argyros, I.K. ; Silva, G.N. . Extending the Applicability of Inexact Gauss-Newton Method for Solving Nonlinear Least Square Problems. Journal of the Korean Mathematical Society, v. 56, p. 311-327, 2019.

6. Argyros, I.K. ; Silva, G.N. . Extending the Kantorovich’s theorem on Newton’s method for solving strongly regular generalized equation, Optimization Letters, v. 13(1), p. 213–226, 2019.

7. Adona, V.A.; Gonçalves, M. L. N.; Melo, J. G. A Partially Inexact Proximal Alternating Direction Method of Multipliers and Its Iteration-Complexity Analysis.  J. Optim. Theory App., 182(2): 640–666,2019 (pdf).

8. Adona, V.A.; Gonçalves, M. L. N.; Melo, J. G..  Iteration-complexity of a generalized alternating direction method of multipliers. Journal of Global Optimization, 73(2):331-348, 2019 (pdf).

9. De Oliveira, F. R.; Ferreira, O. P.; Silva, G. N. Newton’s method with feasible inexact projections for solving constrained generalized equations, Comput. Optim. and Appl.,   v. 72, n. 1, p. 159-177, 2019.  (pdf).

10. Ferreira, O. P.; Németh, S. Z; Xiao, L. On the spherical quasi-convexity of quadratic functions,  Linear Algebra and  Appl., v.562, n. 1,  p. 205-222, 2019. (pdf).

11. Ferreira, O. P.; Németh, S. Z.; On the spherical convexity of quadratic functions,  J. Global Optim.  v. 73, n. 3, p. 537-545, 2019. (pdf).

12. Ferreira, O. P; Louzeiro, M. S.; Prudente, L. F. Iteration-complexity of the subgradient method on Riemannian manifolds with lower bounded curvature, Optimization,v.68, n.4, p. 713-729 , 2019. (pdf).

13. Ferreira, O. P.; Silva, G. N. Inexact Newton's method to Nonlinear function with values in a cone, Applicable Analysis, v. 98, n.8, p. 1461-1477, 2019. (pdf). 

14. Bello Cruz, J.Y., Díaz Millán, R., Phan, H.M. Conditional extragradient algorithms for solving variational inequalities. Pacific Journal of Optimization. v.15, 331--357 (2019).

15.  Bento, G. C., Bitar, S. D. B., Da Cruz Neto, J. X., Oliveira, P. R., De Oliveira Souza, J. C.: Computing Riemannian Center of Mass on Hadamard Manifolds. J. Optim. Theory App.,  v. 183, p. 977-992, 2019. 

16. Díaz Millán R., Lindstrom Scott B., Roshchina V. Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples. BOOK CHAPTERS. Accepted to Special Springer Volume commemorating Jon Borwein, Springer Proceedings in Mathematics and Statistics, 2019. (pdf)

17. Gonçalves, M. L. N.; Melo, J. G.; Monteiro, R. D. C.. Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems.  Pacific journal of optimization, 15(3), 379-398, 2019. (pdf).

 

Publications 2018

1. Lucambio Pérez, L. R.; Prudente, L. F. Non-linear conjugate gradient methods for vector optimization, SIAM J. Optim., v. 28, p. 2690-2720, 2018.

2. Ferreira, O. P.; Silva, G. N. Local convergence analysis of Newton’s method for solving strongly regular generalized equations,  J. Math. Anal. Appl., v.458, n.1, p.481-496, 2018 (pdf).

3. Ferreira, O. P.; Németh, S. Z. . How to project onto extended second order cones. J. Global Optim. , v. 70, p. 707-718, 2018.

4. Bento, G. C.; Ferreira, O. P.; Pereira, Y. R. L. Proximal Point Method for Vector Optimization on Hadamard Manifolds,Operations Research Letters, v.46, n.1, p.13–18, 2018,  (pdf).

5. Bento, G. C.; Ferreira, O. P.; Soubeyran, A; Sousa Junior, V. Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems, J. Optim. Theory Appl.,  v. 177, p. 181-200, 2018. (pdf). 

6. Bento, G. C.; Ferreira, O. P.; Sousa Junior, V. Proximal point method for a special class of nonconvex multiobjective optimization problem, Optim. Lett., v. 12, p. 311–320, 2018. (pdf).

7. Bento, G. C.; Cruz Neto, J. X. ; Santos, P. S. M. ; Souza, S. S. . A weighting subgradient algorithm for multiobjective optimization. Optimization Letters, v. 12, p. 399-410, 2018.

8. Bento, G.C; Bouza Allende, G. ; Pereira, Y. R. L.. A Newton-Like Method for Variable Order Vector Optimization Problems. J. Optim. Theory Appl., , v. 177, p. 201-221, 2018.

9. Bento, G. C.; Cruz Neto, J. X. ; López, G. ; Soubeyran, A. ; Souza, J. C. O. . The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem. SIAM J. Optim.,, v. 28, p. 1104-1120, 2018.

10. Bento, G. C.; da Cruz Neto, J. X ; Meireles, L. V. . Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization of Hadamard Manifolds. J. Optim. Theory Appl. , p. 1-16, 2018.

11. Gonçalves, M. L. N.; Oliveira, F.R..  An inexact Newton-Like gradient method for constrained nonlinear systems. Applied Numerical Mathematics, Vol 132(1), 22-34. 2018  (pdf).

12. Gonçalves, M. L. N. On the pointwise iteration-complexity of a dynamic regularized ADMM with over-relaxation stepsize.  Applied Mathematics and Computation, Vol 336 (1),  315-325, 2018 (pdf).

13. Gonçalves, M. L. N.; Marques Alves, M; Melo, J. G.. Pointwise and ergodic convergence rates of a variable metric proximal ADMM. J. Optim. Theory Appl Vol 177, No.1: pp 448-478, 2018. (pdf)

14. Díaz Millán, R. Two algorithms for solving systems of inclusion problems. Numerical  Algorithms, v. 78, p. 1111-1127, 2018.

Publications 2017

1. Ferreira, O. P.;   Jean-Alexis, Célia; Piétrus, Alain . Metrically regular vector field and iterative processes for generalized equations in Hadamard manifolds, J. Optim. Theory Appl.,  v. 175, p. 624-651, 2017.   (pdf).

2. Ferreira, O. P.; Silva, G. N. Kantorovich's theorem on Newton's method for solving strongly regular generalized equation,  SIAM J. Optim., v. 27 (2), p. 910-926, 2017.(pdf).

3. Gonçalves, M. L. N.; Melo, J. G.; Monteiro, R. D. C.. Improved pointwise iteration-complexity of a regularized ADMM and of a regularized non-Euclidean HPE framework.  SIAM J. Optim., Vol. 27, No. 1 : pp. 379-407, 2017.

4. Bello Cruz, J. Y.; Ferreira, O. P.; Németh, S. Z.; Prudente, L. F., A semi-smooth Newton method for projection equations and linear complementarity problems with respect to the second order cone. Linear Algebra and its Applications 513, 160-181, 2017.

5. Bento, Glaydston C. ; Ferreira, O. P. ; Melo, Jefferson G. . Iteration-Complexity of Gradient, Subgradient and Proximal Point Methods on Riemannian Manifolds. Journal of Optimization Theory and Applications,  v. 173, n.2, p. 548–562, 2017. (pdf).
6. Fernandes, Teles A. ; Ferreira, O. P.; Yuan, JinYun . On the Superlinear Convergence of Newton?s Method on Riemannian Manifolds. Journal of Optimization Theory and Applicationsv, v.173, n.3,  p. 828-843, 2017. (pdf).
7.Bittencourt, Tibério; ; Ferreira, O. P. . Kantorovich's theorem on Newton's method under majorant condition in Riemannian manifolds. Journal of Global Optimization, v. 68, n.2, p.387-411,  2017. (pdf).
8. Díaz Millán, R., Gibali, A. Characterization of orthogonal polynomials - A new proof to Bochner Theorem. BOOK CHAPTERS. Contemporary Mathematics, Complex Analysis and Dynamical Systems VII 699 (2017) 87-101. 

Publications 2016

1. Barrios, J. G.; Bello Cruz, J. Y.; Ferreira, O. P.; Németh, S. Z. A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programming. J. Comput. Appl. Math. 301 (2016), 91-100. 

2. Batista, Edvaldo E. A.; Bento, G. C.; Ferreira, O. P. ; Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds. J. Optim. Theory Appl. 170 (2016), no. 3, 916-931.

3. Bello Cruz, J. Y.; Ferreira, O. P.; Prudente, L. F. On the global convergence of the inexact semi-smooth Newton method for absolute value equation. Comput. Optim. Appl. 65 (2016), no. 1, 93-108.

4. Bento, G. C.; Cruz Neto, J. X.; Lopes, J. O.; Soares, P. A., Jr.; Soubeyran, A. Generalized proximal distances for bilevel equilibrium problems. SIAM J. Optim. 26 (2016), no. 1, 810–830.
5. Bento, G. C. ; da Cruz Neto, J. X.; Oliveira, Paulo Roberto. A new approach to the proximal point method: convergence on general Riemannian manifolds. J. Optim. Theory Appl. 168 (2016), no. 3, 743–755.

6. Gonçalves, M. L. N. Inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant condition. Numer. Algorithms 72 (2016), no. 2, 377–392.

7. Gonçalves, M. L. N.; Melo, Jefferson G. A Newton conditional gradient method for constrained nonlinear systems. Journal of Computational and Applied Mathematics,  311 (2016), 473-483.

8. Bento, G. C.; Cruz Neto, J. X.;  Soubeyran, A.; Sousa Júnior, Valdinês L. de. Dual Descent Methods as Tension Reduction Systems. J. Optim. Theory Appl. 171 (2016), no. 1, 209-227.

9. Bello Cruz, J. Y., Díaz Millán, R. A relaxed-projection splitting algorithm for variational inequalities in Hilbert space. Journal of Global Optimization 65 (2016), no.3,  597-614.

10. Bello Cruz, J. Y.; De Oliveira, W. . On Weak and Strong Convergence of the Projected Gradient Method for Convex Optimization in Real Hilbert Spaces. Numerical Functional Analysis and Optimization, v. 37, p. 129-144, 2016.

11. Bauschke, H. H. ; Bello Cruz, J.Y. ; Nghia, T. A. ; Phan, Hung M. ; Wang, Xianfu. Optimal Rates of Linear Convergence of Relaxed Alternating Projections and Generalized Douglas-Rachford Methods for Two Subspaces. Numerical Algorithms, v. 1, p. 1-44, 2016.

12.Van Ackooij, W. ; Bello Cruz, J.Y. ; Oliveira, W. . A strongly convergent proximal bundle method for convex minimization in Hilbert spaces. Optimization (Print), v. 65, p. 145-167, 2016.

13. Bello Cruz, J. Y.; Nghia, T. A. . On the convergence of the forward-backward splitting method with linesearches. Optimization Methods & Software (Print), v. 1, p. 1-30, 2016.

Publications 2015

1. Barrios, Jorge; Ferreira, O. P. ; Németh, Sándor Z. Projection onto simplicial cones by Picard's method. Linear Algebra Appl. 480 (2015), 27-43

2. Batista, E. E. A.; Bento, G. C.; Ferreira, O. P. An existence result for the generalized vector equilibrium problem on Hadamard manifolds. J. Optim. Theory Appl. 167 (2015), no. 2, 550-557.

3. Bento, G. C.; Ferreira, O. P.; Oliveira, P. R. Proximal point method for a special class of nonconvex functions on Hadamard manifolds. Optimization 64 (2015), no. 2, 289-319. 

4. Bento, G. C.; Soubeyran, A. A generalized inexact proximal point method for nonsmooth functions that satisfies Kurdyka Lojasiewicz inequality. Set-Valued Var. Anal. 23 (2015), no. 3, 501–517.

5. Bento, G. C.; Soubeyran, A. Generalized inexact proximal algorithms: routine's formation with resistance to change, following worthwhile changes. J. Optim. Theory Appl. 166 (2015), no. 1, 172–187.

6. Birgin, E. G.; Martínez, J. M.; Prudente, L. F. Optimality properties of an augmented Lagrangian method on infeasible problems. Comput. Optim. Appl. 60 (2015), no. 3, 609–631.

7. Bittencourt, Tiberio; Ferreira, O. P.  Local convergence analysis of inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds. Appl. Math. Comput. 261 (2015), 28-38.

8. Burachik, Regina S.; Iusem, Alfredo N.; Melo, Jefferson G. The exact penalty map for nonsmooth and nonconvex optimization. Optimization 64 (2015), no. 4, 717–738.

9. Ferreira, O. P. A robust semi-local convergence analysis of Newton's method for cone inclusion problems in Banach spaces under affine invariant majorant condition. J. Comput. Appl. Math. 279 (2015), 318-335. 

10. Ferreira, O. P.; Németh, S. Z. Projection onto simplicial cones by a semi-smooth Newton method. Optim. Lett. 9 (2015), no. 4, 731-741.

11. Gonçalves, M. L. N.; Melo, J. G.; Prudente, L. F. Augmented Lagrangian methods for nonlinear programming with possible infeasibility. J. Global Optim. 63 (2015), no. 2, 297–318.

12. Gonçalves, M. L. N.; Oliveira, P. R. Convergence of the Gauss-Newton method for a special class of systems of equations under a majorant condition. Optimization 64 (2015), no. 3, 577–594.

13. Bello Cruz, J. Y., Díaz Millán, R. A variant of Forward-Backward splitting method for the sum of two monotone operators with a new search strategy. Optimization 64 (2015),  No. 7, 1471-1486.

14. Bello Cruz, J. Y.; Iusem, A. N. . Full convergence of an approximate projection method for nonsmooth variational inequalities. Mathematics and Computers in Simulation (Print), v. 114, p. 2-13, 2015.

Publications 2014
1. Bello Cruz, J. Y.; Bouza Allende, G.; Lucambio Pérez, L. R. Subgradient algorithms for solving variable inequalities. Appl. Math. Comput. 247 (2014), 1052-1063.

2. Ferreira, O. P.; Iusem, A. N.; Németh, S. Z. Concepts and techniques of optimization on the sphere. TOP 22 (2014), no. 3, 1148-1170.

3. Bello Cruz, J. Y.; Lucambio Pérez, L. R. A subgradient-like algorithm for solving vector convex inequalities. J. Optim. Theory Appl. 162 (2014), no. 2, 392-404.

4. Bento, G. C.; Cruz Neto, J. X.; Soubeyran, A. A proximal point-type method for multicriteria optimization. Set-Valued Var. Anal. 22 (2014), no. 3, 557–573.

5. Bento, G. C.; Cruz Neto, J. X. Finite termination of the proximal point method for convex functions on Hadamard manifolds. Optimization 63 (2014), no. 9, 1281–1288.

6. Bento, G. C.; Cruz Neto, J. X.; Oliveira, P. R.; Soubeyran, A. The self regulation problem as an inexact steepest descent method for multicriteria optimization. European J. Oper. Res. 235 (2014), no. 3, 494–502.

7. Bello  Cruz, J. Y., Díaz Millán, R. A direct splitting method for nonsmooth variational inequalities. Journal of Optimization Theory and Application 161 (2014), no. 728-737.

8. Bello Cruz, J. Y.; De Oliveira, W. . Level bundle-like algorithms for convex optimization. Journal of Global Optimization (Dordrecht. Online), v. 59, p. 787-809, 2014.

9. Bauschke, HEINZ H. ; Bello Cruz, J.Y. ; Nghia, TranT.A. ; Phan, Hung M. ; Wang, Xianfu. The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle. Journal of Approximation Theory v. 185, p. 63-79, 2014.

10. Bello Cruz, J. Y.; Bouza Allende, G. . A Steepest Descent-Like Method for Variable Order Vector Optimization Problems. Journal of Optimization Theory and Applications, v. 162, p. 371-391, 2014.

11. Birgin, E. G.; Martínez, J. M.; Prudente, L. F. Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming. J. Global Optim. 58 (2014), no. 2, 207–242.

Publications 2013
1. Ferreira, O. P.; Iusem, A. N.; Németh, S. Z. Projections onto convex sets on the sphere. J. Global Optim. 57 (2013), no. 3, 663-676.

2. Ferreira, O. P.; Gonçalves, M. L. N.; Oliveira, P. R. Convergence of the Gauss-Newton method for convex composite optimization under a majorant condition. SIAM J. Optim. 23 (2013), no. 3, 1757-1783.

3. Da Cruz Neto, J. X.; Da Silva, G. J. P.; Ferreira, O. P.; Lopes, J. O. A subgradient method for multiobjective optimization. Comput. Optim. Appl. 54 (2013), no. 3, 461-472.

4. Bello Cruz, J. Y.; Santos, P. S. M. ; Scheimberg, S. . A Two-Phase Algorithm for a Variational Inequality Formulation of Equilibrium Problems. Journal of Optimization Theory and Applications, v. 159, p. 562-575, 2013.

5. Marques Alves, M.; Melo, J. G. Strong convergence in Hilbert spaces via Γ-duality. J. Optim. Theory Appl. 158 (2013), no. 2, 343–362.

6. Regina S.; Iusem, Alfredo N.; Melo, Jefferson G. An inexact modified subgradient algorithm for primal-dual problems via augmented Lagrangians. J. Optim. Theory Appl. 157 (2013), no. 1, 108–131.

7. Gonçalves, M. L. N. Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition. Comput. Math. Appl. 66 (2013), no. 4, 490–499.

8. Bento, G. C.; Cruz Neto, J. X. A subgradient method for multiobjective optimization on Riemannian manifolds. J. Optim. Theory Appl. 159 (2013), no. 1, 125–137.

9. Bento, G. C.; da Cruz Neto, J. X.; Santos, P. S. M. An inexact steepest descent method for multicriteria optimization on Riemannian manifolds. J. Optim. Theory Appl. 159 (2013), no. 1, 108–124.

10. Bello Cruz, J.Y.. A Subgradient Method for Vector Optimization Problems. SIAM Journal on Optimization (Print), v. 23, p. 2169-2182, 2013.

Publications 2012
1. Ferreira, O. P. ; Silva, Roberto C. M. Local convergence of Newton's method under a majorant condition in Riemannian manifolds. IMA J. Numer. Anal. 32 (2012), no. 4, 1696-1713.

2. Ferreira, O. P.; Németh, S. Z. Generalized isotone projection cones. Optimization 61 (2012), no. 9, 1087-1098.

3. Bento, G. C.; Ferreira, O. P.; Oliveira, P. R. Unconstrained steepest descent method for multicriteria optimization on Riemannian manifolds. J. Optim. Theory Appl. 154 (2012), no. 1, 88-107.

4. Ferreira, O. P.; Svaiter, B. F. A robust Kantorovich's theorem on the inexact Newton method with relative residual error tolerance. J. Complexity 28 (2012), no. 3, 346-363.

5. Ferreira, O. P.; Németh, S. Z. Generalized projections onto convex sets. J. Global Optim. 52 (2012), no. 4, 831-842.

6. Ferreira, O. P.; Gonçalves, M. L. N.; Oliveira, P. R. Local convergence analysis of inexact Gauss-Newton like methods under majorant condition. J. Comput. Appl. Math. 236 (2012), no. 9, 2487-2498.

7. Martínez, J. M.; Prudente, L. F. Handling infeasibility in a large-scale nonlinear optimization algorithm. Numer. Algorithms 60 (2012), no. 2, 263–277.

8. Bento, Glaydston C.; Melo, Jefferson G. Subgradient method for convex feasibility on Riemannian manifolds. J. Optim. Theory Appl. 152 (2012), no. 3, 773–785.

9.Bello Cruz, J. Y.; Iusem, A. N. . An explicit algorithm for monotone variational inequalities. Optimization, v. 61, p. 855-871, 2012.

Publications 2011
1. Bello Cruz, J. Y.; Lucambio Pérez, L. R.; Melo, J. G. Convergence of the projected gradient method for quasiconvex multiobjective optimization. Nonlinear Anal. 74 (2011), no. 16, 5268-5273.

2. Ferreira, O. P.; Gonçalves, M. L. N. Local convergence analysis of inexact Newton-like methods under majorant condition. Comput. Optim. Appl. 48 (2011), no. 1, 1-21.

3. Ferreira, O. P.; Gonçalves, M. L. N.; Oliveira, P. R. Local convergence analysis of the Gauss-Newton method under a majorant condition. J. Complexity 27 (2011), no. 1, 111-125.

4. Ferreira, O. P. Local convergence of Newton's method under majorant condition. J. Comput. Appl. Math. 235 (2011), no. 5, 1515-1522.

5.Bello Cruz, J.Y.; Pijeira, H. ; Márquez, C. ; Urbina, W. . Sobolev-Gegenbauer-type orthogonality and a hydrodynamical interpretation. Integral Transforms and Special Functions, v. 22, p. 711-722, 2011.


6.Bello Cruz, J.Y.; Iusem, A. N. . A Strongly Convergent Method for Nonsmooth Convex Minimization in Hilbert Spaces. Numerical Functional Analysis and Optimization, v. 32, p. 1009-1018, 2011.

Publications 2010
1.  Bello Cruz, J. Y.; Lucambio Pérez, L. R. Convergence of a projected gradient method variant for quasiconvex objectives. Nonlinear Anal. 73 (2010), no. 9, 2917-2922.

2. Bento, G. C.; Ferreira, O. P.; Oliveira, P. R. Local convergence of the proximal point method for a special class of nonconvex functions on Hadamard manifolds. Nonlinear Anal. 73 (2010), no. 2, 564-572.

3. Burachik, R. S.; Iusem, A. N.; Melo, J. G. Duality and exact penalization for general augmented Lagrangians. J. Optim. Theory Appl. 147 (2010), no. 1, 125–140.

4. Burachik, Regina S.; Iusem, Alfredo N.; Melo, Jefferson G. A primal dual modified subgradient algorithm with sharp Lagrangian. J. Global Optim. 46 (2010), no. 3, 347–361.

5. Bello Cruz, J.Y.; Pijeira, H. ; Urbina, W. . On polar Legendre polynomials. The Rocky Mountain Journal of Mathematics, v. 40, p. 2025-2036, 2010.

6. Bello Cruz, J. Y.; Iusem, A. N. . Convergence of direct methods for paramonotone variational inequalities. Computational Optimization and Applications, v. 46, p. 247-263, 2010

Publications 2009
1. Ferreira, O. P.; Oliveira, P. R.; Silva, R. C. M. On the convergence of the entropy-exponential penalty trajectories and generalized proximal point methods in semidefinite optimization. J. Global Optim. 45 (2009), no. 2, 211-227.

2. Ferreira, O. P.  Local convergence of Newton's method in Banach space from the viewpoint of the majorant principle. IMA J. Numer. Anal. 29 (2009), no. 3, 746-759.

3. Ferreira, O. P.; Svaiter, B. F. Kantorovich's majorants principle for Newton's method. Comput. Optim. Appl. 42 (2009), no. 2, 213-229.

4. Bello Cruz, J.Y.; Iusem, A. N. . A Strongly Convergent Direct Method for Monotone Variational Inequalities in Hilbert Spaces. Numerical Functional Analysis and Optimization, v. 30, p. 23-36, 2009.

Publications 2008
1. da Cruz Neto, J. X.; Ferreira, O. P.; Oliveira, P. R.; Silva, R. C. M. Central paths in semidefinite programming, generalized proximal-point method and Cauchy trajectories in Riemannian manifolds. J. Optim. Theory Appl. 139 (2008), no. 2, 227-242.

2. Ferreira, O. P. Dini derivative and a characterization for Lipschitz and convex functions on Riemannian manifolds. Nonlinear Anal. 68 (2008), no. 6, 1517-1528.

Publications 2007
1. da Cruz Neto, J. X.; Ferreira, O. P.; Iusem, A. N.; Monteiro, R. D. C. Dual convergence of the proximal point method with Bregman distances for linear programming. Optim. Methods Softw. 22 (2007), no. 2, 339-360.

Publications 2006
1. da Cruz Neto, J. X.; Ferreira, O. P.; Pérez, L. R. Lucambio; Németh, S. Z. Convex- and monotone-transformable mathematical programming problems and a proximal-like point method. J. Global Optim. 35 (2006), no. 1, 53-69.

2. Ferreira, O. P.  Convexity with respect to a differential equation. J. Math. Anal. Appl. 315 (2006), no. 2, 626-641.

3. Ferreira, O. P.  Proximal subgradient and a characterization of Lipschitz function on Riemannian manifolds. J. Math. Anal. Appl. 313 (2006), no. 2, 587-597.

Publications 2005
1. da Cruz Neto, João X.; Ferreira, O. P. ; Monteiro, Renato D. C. Asymptotic behavior of the central path for a special class of degenerate SDP problems. Math. Program. 103 (2005), no. 3, Ser. A, 487-514.

2. Ferreira, O. P.; Pérez, L. R. Lucambio; Németh, S. Z. Singularities of monotone vector fields and an extragradient-type algorithm. J. Global Optim. 31 (2005), no. 1, 133-151.

Publications 2002
1. Ferreira, O. P.; Oliveira, P. R. Proximal point algorithm on Riemannian manifolds. Optimization 51 (2002), no. 2, 257-270.

2. da Cruz Neto, J. X.; Ferreira, O. P.; Lucambio Pérez, L. R. Contributions to the study of monotone vector fields. Acta Math. Hungar. 94 (2002), no. 4, 307-320.

3. Ferreira, O. P.; Svaiter, B. F. Kantorovich's theorem on Newton's method in Riemannian manifolds. J. Complexity 18 (2002), no. 1, 304-329.

Publications 2000
1. da Cruz Neto, J. X.; Ferreira, O. P. Q-quadratic convergence on Newton's method from data at one point. Int. J. Appl. Math. 3 (2000), no. 4, 441-447.

2. Iusem, Alfredo N.; Pérez, Luis R. Lucambio An extragradient-type algorithm for non-smooth variational inequalities. Optimization 48 (2000), no. 3, 309-332.

3. da Cruz Neto, J. X.; Ferreira, O. P.; Lucambio Pérez, L. R. Monotone point-to-set vector fields. Dedicated to Professor Constantin Udri-te. Balkan J. Geom. Appl. 5 (2000), no. 1, 69-79.

Publications 1999
1. da Cruz Neto, J. X.; Ferreira, O. P.; Lucambio Perez, L. R. A proximal regularization of the steepest descent method in Riemannian manifold. Balkan J. Geom. Appl. 4 (1999), no. 2, 1-8.

Publications 1998
1. Ferreira, O. P.; Oliveira, P. R. Subgradient algorithm on Riemannian manifolds. J. Optim. Theory Appl. 97 (1998), no. 1, 93-104.

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