A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems

Abstract

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Algoritmo abstracto de épsilon-descenso generalizado

“…Las condiciones (2), (3) y (4) del algoritmo 1 las obtenemos directamente de ( 9), ( 10) y (11). Para conseguir la condición (5) vamos a utilizar el siguiente lema.…”

“…La Optimizacíon Matemática esta bastante avanzada en cuanto al estudio de optimizar funciones convexas, y más aún, si estas son suaves; la motivación viene al estudiar funciones que no son ninguna de estas dos cosas, entre otras razones porque eventualmente aparecen funciones, que surgen de modelar aspectos de la vida real, que no son ni convexas ni suaves. (ver para teoría del consumidor [18], [5], [21], [6], dinámica de grupos [11], [7])…”

Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction

“…If the problem nonconvexity is due to the difference of convex (DC) functions, a number of optimization methods known as DC algorithms (DCA) are developed [13,41,48,53]. DCA approximates a nonconvex DC problem by a sequence of convex ones, such that each iteration only involves a convex optimization problem.…”

“…Several DC decomposition and approximation methods have been introduced for different applications [15,50]. Recently, the proximal linearized algorithms for DC programming are proposed to iteratively solve the subproblem, where one of the convex components is replaced by its linear approximation together with a proximal term [13,48]. In [53], extrapolation is integrated into proximal linearized algorithm for possible acceleration of the proximal DCA.…”

Abstract regularized equilibria: application to Becker’s household behavior theory

“…The motivation to consider this kind of regularization comes from application in behavioral sciences using recent Variational Rationality (VR) approach of human dynamics by Soubeyran (2009Soubeyran ( , 2010Soubeyran ( , 2016Soubeyran ( , 2019a. In this context, the regularization term can be seen as a crude formulation of the complex concept of resistance to change; see for instance Bento and Soubeyran (2015), CruzNeto et al (2020), Bento et al (2019, 2018 and Soubeyran and Souza (2020). As a second contribution, we give an application in behavioral sciences of our abstract regularization approach of equilibrium problems.…”