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. Citation July … Read more

A proximal technique for computing the Karcher mean of symmetric positive definite matrices

This paper presents a proximal point approach for computing the Riemannian or intrinsic Karcher mean of symmetric positive definite matrices. Our method derives from proximal point algorithm with Schur decomposition developed to compute minimum points of convex functions on symmetric positive definite matrices set when it is seen as a Hadamard manifold. The main idea … Read more

Dual equilibrium problems: how a succession of aspiration points converges to an equilibrium

We consider an equilibrium problem defined on a convex set, whose cost bifunction may not be monotone. We show that this problem can be solved by the inexact partial proximal method with quasi distance. As an application, at the psychological level of behavioral dynamics, this paper shows two points: i) how a dual equilibrium problem … Read more

A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes

Multiobjective optimization has a significant number of real life applications. For this reason, in this paper, we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used by \citet{conn} to establish … Read more

An interior proximal point method with phi-divergence for Equilibrium Problems

In this paper, we consider the problem of general equilibrium in a ¬†finite-dimensional space on a closed convex set. For solving this problem, we developed an interior proximal point algorithm with phi-divergence. Under reasonable assumptions, we prove that the sequence generated by the algorithm converges to a solution of the Equilibrium Problem, when the regularization … Read more

Learning how to play Nash, potential games and alternating minimization method for structured nonconvex problems on Riemannian manifolds

In this paper we consider minimization problems with constraints. We show that if the set of constaints is a Riemannian manifold of non positive curvature and the objective function is lower semicontinuous and satisfi es the Kurdyka-Lojasiewicz property, then the alternating proximal algorithm in Euclidean space is naturally extended to solve that class of problems. We … Read more

Proximal Point Method for Minimizing Quasiconvex Locally Lipschitz Functions on Hadamard Manifolds

In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the … Read more

Proximal Methods with Bregman Distances to Solve VIP on Hadamard manifolds

We present an extension of the proximal point method with Bregman distances to solve Variational Inequality Problems (VIP) on Hadamard manifolds (simply connected finite dimensional Riemannian manifold with nonpositive sectional curvature). Under some natural assumption, as for example, the existence of solutions of the (VIP) and the monotonicity of the multivalued vector field, we prove … Read more

Proximal point method on Finslerian manifolds and the “Effort Accuracy Trade off”

In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is di fferentiable and satisfi es the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove … Read more

A Proximal Algorithm with Quasi Distance. Application to Habit’s Formation

We consider a proximal algorithm with quasi distance applied to nonconvex and nonsmooth functions involving analytic properties for an unconstrained minimization problem. We show the behavioral importance of this proximal point model for habit’s formation in Decision and Making Sciences. Article Download View A Proximal Algorithm with Quasi Distance. Application to Habit's Formation