scholarly journals A note on minimax optimization problems with an infinite number of constraints

2021 ◽  
Vol 3 (3) ◽  
Keyword(s):  
Infinite Number ◽  
Optimization Problems ◽  
Minimax Optimization

Exact Solutions for Minimax Optimization Problems

2005 ◽  
Vol 112 (5) ◽  
pp. 454
Author(s):  
Francesc Comellas ◽  
J. Luis A. Yebra
Keyword(s):  
Exact Solutions ◽  
Optimization Problems ◽  
Minimax Optimization

A Method for Solving Multi-Objective Optimization Problems Containing an Infinite Number of Parameterized Objectives

2020 ◽  
Author(s):  
Eliot Rudnick-Cohen
Keyword(s):  
Decision Making ◽  
Infinite Number ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Brute Force ◽  
Multi Objective Optimization ◽  
New Approach ◽  
Multi Objective ◽  
Brute Force Approach ◽  
Better Than

Abstract Multi-objective decision making problems can sometimes involve an infinite number of objectives. In this paper, an approach is presented for solving multi-objective optimization problems containing an infinite number of parameterized objectives, termed “infinite objective optimization”. A formulation is given for infinite objective optimization problems and an approach for checking whether a Pareto frontier is a solution to this formulation is detailed. Using this approach, a new sampling based approach is developed for solving infinite objective optimization problems. The new approach is tested on several different example problems and is shown to be faster and perform better than a brute force approach.

scholarly journals On minimax optimization problems

1982 ◽  
Vol 22 (1) ◽  
pp. 227-230 ◽  
Author(s):  
Zvi Drezner
Keyword(s):  
Optimization Problems ◽  
Minimax Optimization

scholarly journals Calmness and Calculus: Two Basic Patterns

2021 ◽  
Author(s):  
Matúš Benko ◽  
Patrick Mehlitz
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary Optimality Conditions ◽  
Generalized Derivatives ◽  
Minimax Optimization ◽  
Cartesian Products ◽  
Calculus Rules ◽  
Set Valued Mappings ◽  
The One ◽  
Derivatives Of

AbstractWe establish two types of estimates for generalized derivatives of set-valued mappings which carry the essence of two basic patterns observed throughout the pile of calculus rules. These estimates also illustrate the role of the essential assumptions that accompany these two patters, namely calmness on the one hand and (fuzzy) inner calmness* on the other. Afterwards, we study the relationship between and sufficient conditions for the various notions of (inner) calmness. The aforementioned estimates are applied in order to recover several prominent calculus rules for tangents and normals as well as generalized derivatives of marginal functions and compositions as well as Cartesian products of set-valued mappings under mild conditions. We believe that our enhanced approach puts the overall generalized calculus into some other light. Some applications of our findings are presented which exemplary address necessary optimality conditions for minimax optimization problems as well as the calculus related to the recently introduced semismoothness* property.

Sign in / Sign up

Export Citation Format

Share Document