Unconstrained optimization reformulation for stochastic nonlinear complementarity problems

Abstract

We present an unconstrained optimization reformulation for the stochastic nonlinear complementarity problem in this paper, which aims at minimizing an expected residual defined by the D-gap function. We discuss the existence of a solution to the unconstrained expected residual minimization (UERM) problem. By the quasi-Monte Carlo method, we obtain the discrete approximations of the UERM problem and prove that every accumulation point of minimizers or stationary points of discrete approximation problem is La minimum or stationary point of the UERM problem. We finally apply the UERM formulation to the traffic equilibrium problem.

Keywords:

• Stochastic nonlinear complementarity problem
• unconstrained expected residual minimization
• quasi-monte carlo method
• traffic equilibrium problem

Mathematics Subject Classification 2010:

• 90C15
• 90C33

Acknowledgments

The authors thank anonymous referees for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported by the National Natural Science Foundation of China [grant numbers: 11571055, 11601437] and the Fundamental Research Funds for the Central Universities [grant number 106112017CDJZRPY0020].