An extension of the Jacobi algorithm for multi-valued mixed complementarity problems

被引:8
作者
Konnov, I. V. [1 ]
机构
[1] Kazan VI Lenin State Univ, Dept Appl Math, Kazan 420008, Russia
关键词
mixed complementarity problem; multi-valued mappings; upper Z-mappings; Jacobi algorithm; existence of solutions;
D O I
10.1080/02331930600662856
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We consider a generalized mixed complementarity problem (MCP) with box constraints and multi-valued cost mapping. We introduce a concept of an upper Z-mapping, which generalizes the well-known concept of the single- valued Z-mapping and involves the diagonal multi-valued mappings, and suggest an extension of the Jacobi algorithm for the above problem containing a composition of such mappings. Being based on its convergence theorem, we establish several existence and uniqueness results. Some examples of the applications are also given.
引用
收藏
页码:399 / 416
页数:18
相关论文
共 21 条
[1]   On the equivalence of extended generalized complementarity and generalized least-element problems [J].
Ansari, QH ;
Lai, TC ;
Yao, JC .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1999, 102 (02) :277-288
[2]  
BAOICCHI C, 1984, VARIATIONAL QUASIVAR
[3]  
COTTLE RW, 1992, LINEAR COMPLEXITY PR
[4]   EQUIVALENCE OF LINEAR COMPLEMENTARITY-PROBLEMS AND LINEAR-PROGRAMS IN VECTOR LATTICE HILBERT-SPACES [J].
CRYER, CW ;
DEMPSTER, MAH .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1980, 18 (01) :76-90
[5]   Engineering and economic applications of complementarity problems [J].
Ferris, MC ;
Pang, JS .
SIAM REVIEW, 1997, 39 (04) :669-713
[6]  
ISAC G, 1992, COMPLEMENTARY PROBLE
[7]  
Konnov I.V., 2002, J. Appl. Math, V2, P289, DOI [10.1155/S1110757X02106012, DOI 10.1155/S1110757X02106012]
[8]  
KONNOV IV, 2003, ISSLEDOVANIYA INFORM, V6, P57
[9]  
Konnov IV., 2001, Combined relaxation methods for variational inequalities
[10]  
LAPIN AV, 2002, COMPUT METH APPL MAT, V2, P26