A New Complementarity Function and Applications in Stochastic Second-Order Cone Complementarity Problems

Guo Sun*, Jin ZHANG, Li Ying Yu, Gui Hua Lin

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)

Abstract

This paper considers the so-called expected residual minimization (ERM) formulation for stochastic second-order cone complementarity problems, which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone. We show that the ERM model has bounded level sets under the stochastic weak R-property. We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications. Then, we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis. Furthermore, we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks.

Original languageEnglish
Pages (from-to)251-283
Number of pages33
JournalJournal of the Operations Research Society of China
Volume7
Issue number2
DOIs
Publication statusPublished - 5 Jun 2019

Scopus Subject Areas

  • Management Science and Operations Research

User-Defined Keywords

  • Complementarity function
  • Error bound
  • Expected Residual Minimization (ERM) model
  • Monte Carlo method
  • Optimal power flow
  • Stochastic second-order cone complementarity problem

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