scholarly journals A Penalty Approach to Optimal Control of Allen-Cahn Variational Inequalities: MPEC-View

2012 ◽  
Vol 33 (11) ◽  
pp. 1321-1349 ◽  
Author(s):  
M. Hassan Farshbaf-Shaker
Keyword(s):  
Optimal Control ◽  
Variational Inequalities ◽  
Penalty Approach

scholarly journals On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 266 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimal Control Theory ◽  
Infinite Dimensional ◽  
Nash Games ◽  
New Class ◽  
Set Valued Mappings ◽  
Differential Variational Inequalities ◽  
Theoretical Developments

A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.

Optimal Control in Some Variational Inequalities

1984 ◽  
Vol 22 (3) ◽  
pp. 466-476 ◽  
Author(s):  
F. Mignot ◽  
J. P. Puel
Keyword(s):  
Optimal Control ◽  
Variational Inequalities
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