随机线性二阶锥互补问题的实值隐拉格朗日法

doi:10.6040/j.issn.1671-9352.0.2021.777

摘要/Abstract

摘要： 为探讨随机二阶锥互补问题的求解方法,利用实值隐拉格朗日法求解随机线性二阶锥互补问题。通过借助于对称锥互补问题中实值隐拉格朗日函数和随机问题的期望残差极小化方法,探讨所得问题解的存在性。由于期望残差极小化模型的目标函数中含有数学期望,故利用蒙特卡罗法对该问题进行近似。证得近似问题最优解序列是依概率1地收敛于期望残差极小化问题的最优解,并且近似问题稳定点序列是依概率1地收敛于期望残差极小化问题的稳定点,为随机二阶锥互补问题提供一种新的求解方法。

关键词: 实值隐拉格朗日函数, 随机二阶锥互补, 期望残差极小化, 近似

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

中图分类号:

O224

王国欣,牛玉俊. 随机线性二阶锥互补问题的实值隐拉格朗日法[J]. 《山东大学学报(理学版)》, 2023, 58(4): 49-54.

WANG Guo-xin, NIU Yu-jun. Real-valued implicit Lagrangian for the stochastic linear second-order cone complementarity problem[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 49-54.

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