A SMOOTHING NEWTON METHOD BASED ON SAMPLE AVERAGE APPROXIMATION FOR A CLASS OF STOCHASTIC GENERALIZED NASH EQUILIBRIUM PROBLEMS

作者：Yuan, Yanhong^*; Zhang, Liwei; Wu, Yue

来源：Pacific Journal of Optimization, 2012, 8(2): 361-386.

• stochastic generalized Nash equilibrium problem
• sample average approximation method
• exponential rate
• Clarke's generalized Jacobian
• smoothing Newton method

In this paper, a type of one stage stochastic generalized Nash equilibrium problem (SGNEP) is solved by the sample average approximation (SAA) method. It is demonstrated that the sequence of Karush-Kuhn-Tucker points of SAA problems converges to a Karush-Kuhn-Tucker point of the true problem with probability one at an exponential rate as the sample size tends to infinity. To implement the SAA method in practice, the smoothing Newton method is introduced. In the case when the expectation constraint functions in the true problem are strongly additive, the nonsingularity of Clarke's generalized Jacobian of the SAA Karush-Kuhn-Tucker system, which is required in the convergence analysis of smoothing Newton method, is demonstrated under the so-called SGNEP-LICQ and SGNEP-SOSC. For this special case, preliminary numerical results are reported to show the efficiency of the method.

• 出版日期2012-4
• 单位大连理工大学; 太原理工大学