JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (4): 49-54.doi: 10.6040/j.issn.1671-9352.0.2021.777

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Real-valued implicit Lagrangian for the stochastic linear second-order cone complementarity problem

WANG Guo-xin, NIU Yu-jun   

  1. School of Mathematics and Physics, Nanyang Institute of Technology, Nanyang 473004, Henan, China
  • Published:2023-03-27

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Abstract: In order to study the solution of stochastic second-order cone complementarity problem, this paper studies the stochastic linear second-order cone complementarity problem by the real-valued implicit Lagrangian function. By using the real-valued implicit Lagrangian for symmetric cone complementarity problems and the expected residual minimization formulation for stochastic problems, the existence of solutions of the obtained problems is discussed. Because the objective function of the expected residual minimization formulation contains mathematical expectation, the problem is approximated by using the Monte Carlo method. It is proved that the optimal solution sequence of the approximate problems converges to the optimal solution of the expected residual minimization problem according to probability 1, and the stable point sequence of the approximate problems converges to the stable point of the expected residual minimization problem with probability 1, which can provide a new method for solving stochastic second order cone complementarity problems.

Key words: real-valued implicit Lagrangian function, stochastic second-order cone complementarity, expected residual minimization, approximation

CLC Number: 

  • O224
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