A smoothing Newton method for generalized Nash equilibrium problems with second-order cone constraints
Yanhong Yuan, Hongwei Zhang, Liwei Zhang · Numerical Algebra Control and Optimization · 2012
We consider a type of generalized Nash equilibrium problems withsecond-order cone constraints. The Karush-Kuhn-Tucker system can beformulated as a system of semismooth equations involving metricprojectors. Furthermore, the smoothing Newton method is given to geta Karush-Kuhn-Tucker point of the problem. The nonsingularity ofClarke's generalized Jacobian of the Karush-Kuhn-Tucker system,which is needed in the convergence analysis of smoothing Newtonmethod, is demonstrated under the so-called constraint nondegeneracycondition in generalized Nash equilibrium problems and pseudo-strongsecond order optimality condition. At last, we take someexperiments, in which the smoothing Newton method is applied.Furthermore, we get the normalized equilibria in theconstraint-shared case. The numerical results show that thesmoothing Newton method has a good performance in solving this typeof generalized Nash equilibrium problems.