# Seminar 2015.1

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Organized by Leandro da Fonseca Prudente

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04/03/2015, 16:00-17:00

Apresentado por: Hugo Vinícius Leão e Silva (Professor Instituto Federal de Educação, Ciência e Tecnologia de Goiás) *Método de Newton aplicado em função real de parâmetro complexo*

Resumo: O trabalho envolve a análise da aplicação do Método de Newton numa função objetivo real de parâmetros complexos relacionada a um problema de processamento de sinais para a rápida convergência das estimativas iniciais fornecidas por um método de otimização global.

11/03/2015, 16:00-17:00

Luis Roman Lucambio Pérez (Professor IME/UFG)

Resumo:

18/03/2015, 16:00-17:00

Yuri Rafael Leite Pereira (Phd Student IME/UFG)**Newton's Method in Variable Order**

Abstract: In this talk we will make a generalization of the Newton's method w.r.t. structures variable order.

25/03/2015, 16:00-17:00

José Yunier Bello Cruz (Professor IME/UFG)*On the convergence of the forward-backward iteration*

Abstract: In this talk we present the convergence and complexity of the forward-backward iteration for many different problems. Several open problems will be analyzed.

01/04/2015, 16:00-17:00

Jorge Barrios Ginart (Aluno de pós-doutorado do IME/UFG)*A semi-smooth Newton method for solving convex quadratic programming problem under simplicial cone constraint.*

Abstract: In this work the simplicial cone constrained convex quadratic programming problem is studied. The optimality conditions of this problem consist in a linear complementarity problem. This fact, under a suitable condition, leads to an equivalence between the simplicial cone constrained convex quadratic programming problem and the one of finding the unique solution of a nonsmooth system of equations. It is shown that a semi-smooth Newton method applied to this nonsmooth system of equations is always well defined and under a mild assumption on the simplicial cone the method generates a sequence that converges linearly to its solution. Besides, we also show that the generated sequence is bounded for any starting point and a formula for any accumulation point of this sequence is presented. The presented numerical results suggest that this approach achieves accurate solutions to large problems in few iterations.

08/04/2015, 16:00-17:00

Paulo Roberto Oliveira (COPPE/UFRJ)*A STRONGLY POLYNOMIAL-TIME ALGORITHM FOR THE STRICT HOMOGENEOUS LINEAR-INEQUALITY FEASIBILITY PROBLEM*

Abstract: A strongly polynomial-time algorithm is proposed for the strict homogeneous linear-inequality feasibility problem in the positive outhunt, that is, to obtain x ? Rn, such that Ax > 0, x > 0, for an m x n matrix A. This algorithm requires O(p) iterations and O(m2 (n+p)) arithmetical operations to ensure that the distance between the solution and the iteration is 10-p . No matrix inversion is needed. An extension to the non-homogeneous linear feasibility problem is presented.

15/04/2015, 16:00-17:00

Orizon Pereira Ferreira (Professor IME/UFG)*A semi-smooth Newton method for solving convex programming problem under simplicial cone constraint*

Abstract: The purpose of this talk is to motivate and describe a new approach for solving a special class of constrained convex programming problems, by using the semi-smmooth Newton's method.

29/04/2015, 16:00-17:00

Glaydston Carvalho Bento (Professor IME/UFG)*An Approach on the Proximal Point Method on Riemannian Manifolds*

Abstract: In this talk will be presented an approach on the proximal point method in Riemannian context. In particular, without any restrictive assumption about the sign of the sectional curvature of the manifold, is obtained full convergence of any bounded sequence generated from the proximal point method, when the objective function satisfies the Kurdyka-Lojasiewicz inequality. Moreover, is extended the applicability of the proximal point method to solving any problem which may be formulated as the of minimizing a definable function (e.g. analytic) restricted to a compact manifold whose sign of the sectional curvature not is necessarily constant.

06/05/2015, 16:00-17:00

Leandro da Fonseca Prudente (Professor IME/UFG)*Augmented Lagrangian methods for nonlinear programming with possible infeasibility*

Abstract: We consider a nonlinear programming problem for which the constraint set may be infeasible. We propose an algorithm based on a large family of augmented Lagrangian functions and, accepting inexact global solutions of the subproblems, analyze its convergence properties taking into account the possible infeasibility of the problem. In a finite number of iterations, the algorithm stops detecting the infeasibility of the problem or finds an approximate feasible/optimal solution with any required precision. We present some numerical experiments illustrating the applicability of the algorithm for different Lagrangian/penalty functions proposed in the literature.

13/05/2015, 16:00-17:00

Edvaldo E. A. Batista (Phd Student IME/UFG)**Um algoritmo inexato para o problema de otimização restrito em variedades de Hadamard**

Resumo: Apresentaremos o problema de otimização restrito em variedades, bem como um método de ponto proximal para soluciona-lo.

20/05/2015, 16:00-17:00

Gilson do Nascimento Silva (Phd Student IME/UFG)*A robust Kantorovich's Theorem for Inexact Newton's method for cone inclusion problems under affine invariant majorant condition*

Abstract: A semi-local analysis of inexact Newton's method for solving nonlinear inclusion problems in Banach space is presented. The robust convergence of the method and results on the convergence rate are established.

03/06/2015, 16:00-17:00

Valdinês Leite de Sousa Júnior (Phd Student IME/UFG)*Proximal point method for a special class of nonconvex multiobjective optimization problem*

Abstract: The proximal method for special class of nonconvex multiobjective functions is studied in this paper. We show that the method is well defined and the accumulation points of any generated sequence, if any, are Pareto-Clarke critical points. Moreover, under additional assumptions, we show full convergence of the generated sequence.

10/06/2015, 16:00-17:00

Paulo César da Silva Júnior (Phd Student IME/UFG)**On the convergence of the proximal forward-backward splitting method with linesearches**

Abstract: In this talk we focus on the convergence analysis of the proximal forward-backward splitting method for solving nonsmooth optimization problems in Hilbert spaces when the objective function is the sum of two convex functions. Assuming that one of the functions is Fréchet differentiable and using two new linesearches, the weak convergence is established without any Lipschitz continuity assumption on the gradient. Furthermore, we obtain many complexity results of cost values at the iterates when the stepsizes are bounded below by a positive constant. A fast version with linesearch is also provided.

17/06/2015, 16:00-17:00

Abssan Matuzinhos de Moura (Aluno de mestrado do IME/UFG)*A variante Barzilai-Borwein do Método do Gradiente*

Resumo: Devido a sua simplicidade e eficiência, a variante do Método do Gradiente proposta por Barzilai e Borwein, em 1988, chama a atenção. Este algoritmo gera uma sequencia com valores funcionais não monótona, e a analise de convergência da sequencia assim gerada se revela muito complexa e fora dos padrões. Neste seminário apresentaremos o estudo realizado por Y.H. Dai, publicado em 2013, mostrando que para o caso de duas variáveis e quando a função objetivo for quadrática e convexa, temos convergência R-superliner em no máximo três iterados consecutivas.

24/06/2015, 16:00-17:00

Luis Roman Lucambio Pérez (Professor IME/UFG)

Resumo: