解一类变分不等式问题的区域分割算法  

A region segmentation algorithm for solving a class of variational inequality problems

作　　者：何非 商玉凤 吴睿 李可雨阳 HE Fei;SHANG Yu-feng;WU Rui;LI Ke-yu-yang(Department of Mathematics,Changchun University of Finance and Economics,Changchun 130122,China;Department of Finance and Economics,Shanghai Lida University,Shanghai 201608,China;School of Business,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]长春财经学院数学教研部,吉林长春130122 [2]上海立达学院财经学院,上海201608 [3]郑州大学商学院,河南郑州450001

出　　处：《东北师大学报（自然科学版）》2024年第4期35-41,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：吉林省自然科学基金资助项目(20200201274JC);吉林省教育厅科学技术研究项目(JJKH20231409KJ)。

摘　　要：研究了带洞非凸域上变分不等式问题,利用添加动约束函数方法,将带洞非凸可行域分割成非凸不带洞可行域,证明了它们之间解的关系.在非凸不带洞可行域上给出了易于选取初始点的动约束同伦算法,证明了同伦路径是存在的、有界的和收敛的,并用数值算例验证了算法的有效性.The variational inequality problem on non-convex domain with holes is studied.The method of adding dynamic constraint function to partition the non-convex feasible domain with holes into non-convex feasible domains without holes is used.The relationship of the solutions between them and the dynamic constraint homotopy algorithm on non-convex without holes which is easy to select the initial point are given.It is proved that the homotopy paths are existent,bounded and convergent.The validity of the algorithm is verified by numerical examples.

关 键 词：变分不等式 大范围收敛 同伦算法 

分 类 号：O221.2[理学—运筹学与控制论]