ProfOptimization2016

Seminar 2014.1

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Organized by  Max Leandro Nobre Gonçalves
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14/03/2014, 14:00 -15:00
Orizon Pereira Ferreira (Professor IME/UFG)       
 A semi-local  convergence analysis   of Newton's  method  for cone inclusion problems in Banach spaces under   affine invariant   majorant condition
Abstract: A semi-local  analysis of Newton's method for solving nonlinear inclusion problems in Banach space  is presented in this paper. Under a affine majorant condition on the nonlinear function which is associated to the inclusion problem, the  convergence of the method and results on the convergence rate are established. Using this result we show that the  analysis of the Newton's method for solving nonlinear inclusion problems under affine Lipschitz-like and  affine Smale's  conditions can be obtained as a special case of the general theory. Besides for the degenerate cone,  which the nonlinear inclusion  becomes  a nonlinear equation, ours analysis retrieve the classical results on local analysis of Newton's method.

28/03/2014, 14:00 -15:00
Reinier Diaz Millan, (Phd Student IME/UFG)   
Conditional Extragradient method for variational inequalities, part I
Absract:  We propose a conceptual algorithm for solving the constrained variational inequality problem (VIP). It contains variants improving the convergence of the important previous extragradient's variants for VIP. The proposed conceptual algorithm contains basically two stages.The .rst part of our approach contains two di erent linesearch one along the boundary of the feasible set and the another one along the feasible direction bring a suitable halfspace separation the current point of the solution set. These linesearch uses non-vanish vectors of the normal cone exploring strongly the structure of the VIP avoiding zigzagging. Furthermore, especial realizations of the variants of the conceptual algorithm, for example if is chosen all vector in the normal cone as zero, are related with important variants of the extragradient method for solving VIP.The second part of the conceptual algorithm consists in special projection steps bringing several variants with di erent features. The convergence analysis of the proposed scheme is given assuming a weaker condition which implies pseudomonotonicity on the operator.

04/04/2014, 14:00 -15:00
Reinier Diaz Millan, (Phd Student IME/UFG)   
Conditional Extragradient method for variational inequalities, part II
Absract:  We propose a conceptual algorithm for solving the constrained variational inequality problem (VIP). It contains variants improving the convergence of the important previous extragradient's variants for VIP. The proposed conceptual algorithm contains basically two stages.The .rst part of our approach contains two di erent linesearch one along the boundary of the feasible set and the another one along the feasible direction bring a suitable halfspace separation the current point of the solution set. These linesearch uses non-vanish vectors of the normal cone exploring strongly the structure of the VIP avoiding zigzagging. Furthermore, especial realizations of the variants of the conceptual algorithm, for example if is chosen all vector in the normal cone as zero, are related with important variants of the extragradient method for solving VIP.The second part of the conceptual algorithm consists in special projection steps bringing several variants with di erent features. The convergence analysis of the proposed scheme is given assuming a weaker condition which implies pseudomonotonicity on the operator.

11/04/2014, 14:00 -15:00
Jurandir A. Lopes, (Professor da UFPI)   
An proximal point method with generalized distances for Equilibrium Problems
Abstrac: In this talk, we consider the problem of general equilibrium in a finite- dimensional space on a closed convex set. For solving this problem, we developed an proximal point algorithm with generalized distances. Under reasonable assumptions, we prove that the sequence generated by the algorithm converges to a solution of the Equilibrium Problem, when the regularization parameters are bounded.  

25/04/2014, 14:00 -15:00
Glaydston de Carvalho Bento (Professor IME/UFG)   
A Proximal Point-Type Method for Multicriteria Optimization
Abstrac:  In this seminar will be presented a proximal point algorithm for multicriteria optimization. With respect to the  convergence analysis, firstly we show that, for any sequence generated from our algorithm, each accumulation point is a Pareto critical point for the multiobjective function. A more significant novelty here is the full convergence for quasi-convex functions.  In the  convex or pseudo-convex cases, is proved convergence to a weak Pareto optimal point. Another contribution is to consider a variant of our algorithm,  obtaining the iterative step through an unconstrained subproblem. Then,  we show that any sequence generated by this new algorithm attains a Pareto optimal point after a finite number of iterations under the assumption that the weak Pareto optimal set is weak sharp for the multiobjective problem.

09/05/2014, 14:00 -15:00
Luis Roman Lucambio Pérez  (Professor IME/UFG)
Métodos do gradiente conjugados não-linear para otimização vetorial
Resumo: Apresentaremos como alguns resultados iniciais sobre os métodos do gradiente conjugados não-linear podem ser estendidos para problemas de otimização vetorial.

16/05/2014, 14:00 -15:00
Jefferson D. G. de Melo(Professor IME/UFG)
Detectando inviabilidade via função Lagrangiana aumentada
Resumo:  Neste seminário consideraremos um problema de programação não-linear com o conjunto de restrições possivelmente inviável. Estudaremos uma classe de funções Lagrangianas aumentadas  aplicada a este problema. Mostraremos que os pontos limites da sequencia primal gerada pelo método Lagrangiano aumentado  minimiza uma medida de inviabilidade.

23/05/2014, 14:00 -15:00
Jorge Barrios Ginart(Aluno de pós-doutorado do IME/UFG)
Retrospective Analysis of the Dengue 3 Epidemic, Havana, 2001
Abstract: Outbreaks of dengue epidemic in different parts of the world have become a health problem. The interests of the health authorities and Cuban scientists to prevent and control the epidemic have led to several investigations. In work we formulate a model to study the evolution dynamics of an epidemic outbreak of dengue fever. The models take into account interaction of human and mosquito populations as well as vertical transmission in the mosquito population. The model was validated by a retrospective analysis of Dengue 3 epidemic, which occurred in Havana City in 2001.

30/05/2014, 14:00 -15:00
Leandro F. Prudente (Professor IME/UFG)
Numerical comparison of Augmented Lagrangian algorithms for nonconvex problems
Abstract: Augmented Lagrangian algorithms are very popular tools for solving nonlinear programming problems. At each outer iteration of these methods a simpler optimization problem is solved, for which efficient algorithms can be used, especially when the problems are large. The most famous Augmented Lagrangian algorithm for minimization with inequality constraints is known as Powell-Hestenes-Rockafellar (PHR) method. The main drawback of PHR is that the objective function of the subproblems is not twice continuously differentiable. This is the main motivation for the introduction of many alternative Augmented Lagrangian methods. Most of them have interesting interpretations as proximal point methods for solving the dual problem, when the original nonlinear programming problem is convex. In this paper a numerical comparison between many of these methods is performed using all the suitable problems of the CUTE collection.

06/06/2014, 14:00 -15:00
Valdinês Leite de Sousa Júnior, (Phd Student IME/UFG)   
Convergence to equilibrium for discretized gradient-like systems with analytic features
Abstract:  We give general conditions which guarantee that the sequence generated by a descent algorithm converges to an equilibrium point. The convergence result is based on the  Lojasiewicz gradient inequality; optimal convergence rates are also derived, as well as a stability result. We show how our results apply to a large variety of standard time discretizations of gradient-like flows. Schemes with variable time step are considered, and optimal conditions on the maximal stepsize are derived. Applications to time and space discretizations of the Allen-Cahn equation, the Sine-Gordon equation, and a damped wave equation, are given.

13/06/2014, 14:00 -15:00
Gilson do Nascimento Silva, (Phd Student IME/UFG)  
O algoritmo do ponto proximal em espaços métricos
Resumo: O objetivo principal deste seminário será introduzir o algoritmo de ponto proximal em espaços
métricos geodésicos de curvatura não-positiva, chamado espaços CAT(0), e provar convergência
fraca deste algoritmo. Espaços CAT(0) inclui espaços de Hibert, R-tree e também variedades Riemanniana completa simplesmente conexa de curvatura seccional não-positiva e muitos outros espaços importantes. Sob hipótese adicional será mostrado convergência forte do algoritmo.

27/06/2014, 14:00 -15:00
Edvaldo E. A. Batista  (Phd Student IME/UFG)
Um resultado de existência para o problema de equilíbrio vetorial generalizado em variedades Riemannianas
Resumo: Neste seminário  consideraremos o problema de equilíbrio vetorial generalizado (PEVG) em variedades Riemannianas. Um resultado de existência sob hipóteses razoáveis será apresentado, mediante a utilização de uma versão do teorema de KKM no contexto Riemanniano, e vários resultados de existência para importantes problemas de otimização serão obtidos como caso particular.

11/07/2014, 14:00 -15:00
Yuri  (Phd Student IME/UFG)  
Método do Gradiente para Otimização Vetorial em Variedades Riemannianas
Resumo: Neste seminário, apresentaremos o método do gradiente com regra de Armijo para problema de otimização vetorial no contexto Riemanniano. Provaremos que cada ponto de acumulação satisfaz condição necessária de K-otimalidade. Além disso, assumindo K-quasiconvexidade das função vetorial e curvatura não negativa da variedade Riemanniana, provaremos a convergência total  da sequência a um ponto K-crítico.

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