Minimax Theorems for Locally Lipschitz Functionals and Applications

2001 ◽  
pp. 173-206
Author(s):  
Maria do Rosário Grossinho ◽  
Stepan Agop Tersian
Keyword(s):  
Minimax Theorems ◽  
Locally Lipschitz

scholarly journals No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints

2021 ◽  
Author(s):  
Giovanni Fusco ◽  
Monica Motta
Keyword(s):  
Original Problem ◽  
State Constraints ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Continuous Data ◽  
Lipschitz Continuous ◽  
Extended Sense ◽  
Unbounded Controls ◽  
Locally Lipschitz ◽  
Optimal Impulsive Control

AbstractIn this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained Maximum Principle ensures that there is no gap between the infima of the original problem and of its extension. Furthermore, we translate such relation into verifiable sufficient conditions for normality in the form of constraint and endpoint qualifications. Links between existence of an infimum gap and normality in impulsive control have previously been explored for problems without state constraints. This paper establishes such links in the presence of state constraints and of an additional ordinary control, for locally Lipschitz continuous data.

scholarly journals Topological minimax theorems

1984 ◽  
Vol 91 (3) ◽  
pp. 377-377 ◽  
Author(s):  
Michael A. Geraghty ◽  
Bor-Luh Lin
Keyword(s):  
Minimax Theorems

An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Fouzia Amir ◽  
Ali Farajzadeh ◽  
Jehad Alzabut
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Convergence Result ◽  
Proximal Method ◽  
Pareto Solution ◽  
Multiobjective Optimization Problems ◽  
Locally Lipschitz ◽  
The Cost ◽  
Constrained Multiobjective Optimization

Abstract Multiobjective optimization is the optimization with several conflicting objective functions. However, it is generally tough to find an optimal solution that satisfies all objectives from a mathematical frame of reference. The main objective of this article is to present an improved proximal method involving quasi-distance for constrained multiobjective optimization problems under the locally Lipschitz condition of the cost function. An instigation to study the proximal method with quasi distances is due to its widespread applications of the quasi distances in computer theory. To study the convergence result, Fritz John’s necessary optimality condition for weak Pareto solution is used. The suitable conditions to guarantee that the cluster points of the generated sequences are Pareto–Clarke critical points are provided.

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