6 papers · 1 filter
Proximity operator characterization for abstract convex functions
Ewa Bednarczuk, The Hung Tran
We consider proximity operator as a selector of the subgradient in the context of abstract convexity and characterize its properties in term of minimization problems. We also inves…
Primal-Dual algorithms for Abstract convex functions with respect to quadratic functions
Ewa Bednarczuk, The Hung Tran
We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the…
Primal-dual algorithm for weakly convex functions under sharpness conditions
Ewa Bednarczuk, The Hung Tran, Monika Syga
We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap…
Outer Approximation Scheme for Weakly Convex Constrained Optimization Problems
Ewa M. Bednarczuk, Giovanni Bruccola, Jean-Christophe Pesquet +1
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solvi…
Forward-Backward algorithms for weakly convex problems
Ewa Bednarczuk, Giovanni Bruccola, Gabriele Scrivanti +1
We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one…
Proximal Algorithms for a class of abstract convex functions
Ewa Bednarczuk, Dirk Lorenz, The Hung Tran
In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an a…