Fisher市场均衡问题的新全牛顿步可行内点算法  

A New Full-Newton Step Feasible Interior-Point Algorithm for Solving the Fisher Market Equilibrium Problem

作　　者：杨绮丽 迟晓妮[2] 张所滨[3] 万仲平[4] YANG Qili;CHI Xiaoni;ZHANG Suobin;WAN Zhongping(Guangxi Key Laboratory of Cryptography and Information Security,School of Mathematics and Computing Science·Guilin University of Electronic Technology;Guangxi Key Laboratory of Automatic Detection Tech no logy and Instruments·School of Mathematics and Computing Science.Guilin University of Electronic Technology;Institute of Scientific Research and Development,Guilin University of Electronic Technology,Guilin Guangxi 541004;School of Mathematics and Statistics,Wuhan University.Wuhan 430072,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院广西密码学与信息安全重点实验室 [2]桂林电子科技大学数学与计算科学学院广西自动检测技术与仪器重点实验室 [3]桂林电子科技大学科学技术发展研究院,广西桂林541004 [4]武汉大学数学与统计学院,武汉430072

出　　处：《重庆师范大学学报（自然科学版）》2022年第2期15-21,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11861026;No.11871383);广西自然科学基金(No.2021GXNSFAA220034);广西密码学与信息安全重点实验室研究课题(No.GCIS201819);广西自动检测技术与仪器重点实验室基金(No.YQ18112)。

摘　　要：【目的】基于光滑中心路径的等价变换,提出一种新的求解Fisher市场均衡问题的线性权互补(Weighted linear complementarity problem, WLCP)模型的全牛顿步可行内点算法。【方法】扰动WLCP,构造光滑中心路径的新代数等价形式,运用牛顿法得到新搜索方向,从而提出求解Fisher市场均衡问题的全牛顿步可行内点算法。【结果】算法采用全牛顿步避免线搜索,提高计算效率,且具有可行性和多项式复杂度。【结论】初步数值结果表明算法有效。[Purposes]Based on the equivalent transformation of smooth central path, a new full-Newton step feasible interior-point algorithm is presented to solve the weighted linear complementarity model of the Fisher market equilibrium problem. [Methods] By perturbing WLCP, the new algebraic equivalent transformation of smooth central path is constructed, and a new search direction by Newton’s method is obtained. Then a full-Newton step feasible interior-point algorithm for solving the Fisher market equilibrium problem is proposed. [Findings] The algorithm uses the full-Newton steps to avoid linear search and improve computational efficiency. It shows the feasibility and polynomial complexity of the algorithm. [Conclusions] Preliminary numerical results indicate that the algorithm is effective.

关 键 词：Fisher市场均衡问题 线性权互补 内点算法 中心路径 全牛顿步 

分 类 号：O221[理学—运筹学与控制论]