A penalty scheme and policy iteration for nonlocal HJB variational inequalities with monotone nonlinearities

2021 ◽  
Vol 93 ◽  
pp. 199-213
Author(s):  
Christoph Reisinger ◽  
Yufei Zhang
Keyword(s):  
Variational Inequalities ◽  
Policy Iteration

scholarly journals A policy iteration algorithm for nonzero-sum stochastic impulse games

2019 ◽  
Vol 65 ◽  
pp. 27-45
Author(s):  
René Aïd ◽  
Francisco Bernal ◽  
Mohamed Mnif ◽  
Diego Zabaljauregui ◽  
Jorge P. Zubelli
Keyword(s):  
Nash Equilibrium ◽  
Numerical Methods ◽  
Variational Inequalities ◽  
Convergence Analysis ◽  
Policy Iteration ◽  
Iteration Algorithm ◽  
Value Functions ◽  
Numerical Tests ◽  
Wide Range ◽  
Policy Iteration Algorithm

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods available, to the best of our knowledge. Our method relies on the recently introduced characterisation of the value functions and Nash equilibrium via a system of quasi-variational inequalities. While our algorithm is heuristic and we do not provide a convergence analysis, numerical tests show that it performs convincingly in a wide range of situations, including the only analytically solvable example available in the literature at the time of writing.

Variational and Quasi-Variational Inequalities in Mechanics

2007 ◽  
Author(s):  
Alexander S. Kravchuk ◽  
Pekka J. Neittaanmäki
Keyword(s):  
Variational Inequalities

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.

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