A smoothing newton method for generalized nash equilibrium problems with second-order cone constraints

Indexed by:期刊论文

Journal:Numerical Algebra, Control and Optimization

Included Journals:Scopus

Volume:2

Issue:1

Page Number:1-18

ISSN No.:21553289

Abstract:We consider a type of generalized Nash equilibrium problems with second-order cone constraints. The Karush-Kuhn-Tucker system can be formulated as a system of semismooth equations involving metric projectors. Furthermore, the smoothing Newton method is given to get a Karush-Kuhn-Tucker point of the problem. The nonsingularity of Clarke's generalized Jacobian of the Karush-Kuhn-Tucker system, which is needed in the convergence analysis of smoothing Newton method, is demonstrated under the so-called constraint nondegeneracy condition in generalized Nash equilibrium problems and pseudostrong second order optimality condition. At last, we take some experiments, in which the smoothing Newton method is applied. Furthermore, we get the normalized equilibria in the constraint-shared case. The numerical results show that the smoothing Newton method has a good performance in solving this type of generalized Nash equilibrium problems.

Date of Publication:2012-01-01