Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications

Yang, Zhen-Ping1; Zhang, Jin2; Zhu, Xide1,3; Lin, Gui-Hua1

2019-05-15

10.1016/j.cam.2018.12.013

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   影响因子和分区

0377-0427

1879-1778

This paper considers a class of stochastic complementarity problems (SCP). Different from the classical complementarity problems, the SCP contains a mathematical expectation, which may not be evaluated in an explicit form in general. We combine an interior-point algorithm for deterministic cases with the well-known sample average approximation (SAA) techniques to present an SAA-based infeasible interior-point algorithm for the SCP. We investigate the convergence properties and computational complexity of the proposed algorithm under mild assumptions. Then, we extend these results to a class of mixed SCPs. Furthermore, we apply the proposed algorithms to solve a stochastic natural gas transmission problem and a stochastic oligopoly model. Preliminary numerical experiments indicate that the proposed approach is competitive with some existing methods. (C) 2018 Elsevier B.V. All rights reserved.

Nonlinear programming Stochastic complementarity problem Sample average approximation Infeasible interior-point algorithm Natural gas transmission and oligopoly models

SCI ; EI

英语

其他

Humanity and Social Science Foundation of Ministry of Education of China[15YJA630034]

Mathematics

Mathematics, Applied

WOS:000458713000027

ELSEVIER SCIENCE BV

20185306322588

Approximation algorithms ; Competition ; Natural gas ; Nonlinear programming ; Numerical methods ; Stochastic systems

Gas Fuels:522 ; Industrial Economics:911.2 ; Mathematics:921 ; Numerical Methods:921.6 ; Probability Theory:922.1 ; Systems Science:961

MATHEMATICS

Web of Science

1.Shanghai Univ, Sch Management, Shanghai 200444, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
3.Yokohama Natl Univ, Fac Business Adm, Hodogaya Ku, 79-4 Tokiwadai, Yokohama, Kanagawa 2408501, Japan

Yang, Zhen-Ping,Zhang, Jin,Zhu, Xide,et al. Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2019,352:382-400.

Yang, Zhen-Ping,Zhang, Jin,Zhu, Xide,&Lin, Gui-Hua.(2019).Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,352,382-400.

Yang, Zhen-Ping,et al."Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 352(2019):382-400.