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Augmented Lagrangian methods for optimal control problems governed by mixed quasi‐equilibrium problems with applications
Author(s) -
Chadli Ouayl,
Ansari Qamrul Hasan,
AlHomidan Suliman
Publication year - 2021
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2722
Subject(s) - augmented lagrangian method , variational inequality , optimal control , mathematics , lagrangian , duality (order theory) , mathematical optimization , lagrangian relaxation , control (management) , dual (grammatical number) , obstacle , computer science , literature , artificial intelligence , political science , law , discrete mathematics , art
The main goal of this article is to study a general augmented Lagrangian method for optimal control problems governed by mixed (quasi‐)equilibrium problems. We establish zero duality gap properties between a primal problem and its augmented Lagrangian dual problem. As a consequence, we give some existence results for optimal control problem governed by evolutionary quasi‐variational inequalities. An application to optimal control of obstacle problems described by quasi‐hemivariational inequalities is studied. The results obtained in this article are new and improves considerably many recent results in literature.