Smoothing Measure with Lipschitz Constant in a Quadratic Augmented Lagrangian Algorithm
Smoothing Measure with Lipschitz Constant in a Quadratic Augmented Lagrangian Algorithm ArticleDownload View PDF
Lennin Mallma Ramirez
Smoothing l1-exact penalty method for intrinsically constrained Riemannian optimization problems
This paper deals with the Constrained Riemannian Optimization (CRO) problem, which involves minimizing a function subject to equality and inequality constraints on Riemannian manifolds. The study aims to advance optimization theory in the Riemannian setting by presenting and analyzing a penalty-type method for solving CRO problems. The proposed approach is based on techniques that involve … Read more
On the global convergence of a general class of augmented Lagrangian methods
In [E. G. Birgin, R. Castillo and J. M. MartÃnez, Computational Optimization and Applications 31, pp. 31-55, 2005], a general class of safeguarded augmented Lagrangian methods is introduced which includes a large number of different methods from the literature. Besides a numerical comparison including 65 different methods, primal-dual global convergence to a KKT point is … Read more
The Hyperbolic Augmented Lagrangian Algorithm
The hyperbolic augmented Lagrangian algorithm (HALA) is introduced in the area of continuous optimization for solving nonlinear programming problems. Under mild assumptions, such as: convexity, Slater’s qualification and differentiability, the convergence of the proposed algorithm is proved. We also study the duality theory for the case of the hyperbolic augmented Lagrangian function. Finally, in order … Read more
Nonmonotonicity and Quasiconvexity on Equilibrium Problems
In this note, some results are introduced considering the assumptions of quasiconvexity and nonmonotonicity, finally an application and an idea to solve the quasiconvex equilibrium problem are presented considering these new results. ArticleDownload View PDF
An Inexact Proximal Method with Proximal Distances for Quasimonotone Equilibrium Problems
In this paper we propose an inexact proximal point method to solve equilibrium problem using proximal distances and the diagonal subdi erential. Under some natural assumptions on the problem and the quasimonotonicity condition on the bifunction, we prove that the sequence generated for the method converges to a solution point of the problem. CitationReport01-2016-PESC-COPPE-UFRJArticleDownload View PDF
An Inexact Proximal Algorithm for Pseudomonotone and Quasimonotone Variational Inequalities
In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generates by the algorithm is convergent for the pseudomonotone case and weakly convergent for the quasimonotone ones. This approach unifies the … Read more
An Inexact Proximal Method for Quasiconvex Minimization
In this paper we propose an inexact proximal point method to solve constrained minimization problems with locally Lipschitz quasiconvex objective functions. Assuming that the function is also bounded from below, lower semicontinuous and using proximal distances, we show that the sequence generated for the method converges to a stationary point of the problem. CitationJuly 2013ArticleDownload … Read more