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A smoothing Newton method for generalized Nash equilibrium problems with second-order cone constraints

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  • 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 pseudo-strong 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.
    Mathematics Subject Classification: Primary: 91A06; Secondary: 91-08, 90C90.


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