On least element problems for feasible sets in vector complementarity problems

Mathematical Methods of Operations Research

Volumn 60, Issue 3, 2004, Pages 369-377

  Fang, Ya Ping ^a   Huang, Nan Jing ^a  

^a SICHUAN UNIVERSITY   (China)

Author keywords

Feasible set; Least element problem; Strictly pseudomonotone map; Vector complementarity problem; Vector variational inequality; Z map

Indexed keywords

LINEAR PROGRAMMING; MATHEMATICAL MODELS; PROBLEM SOLVING; SET THEORY; VECTORS;

LEAST ELEMENT PROBLEMS; VECTOR VARIATIONAL INEQUALITY; Z-MAPS;

OPERATIONS RESEARCH;

EID: 10844238005     PISSN: 14322994     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001860400375     Document Type: Article

References (22)

1. Ansari QH, Lai TC, Yao JC (1999) On the equivalence of extended generalized complementarity and generalized least-element problems. J. Optim. Theory Appl. 102(2):277-288
2. Chen GY (1992) Existence of solutions for a vector variational inequality: an extension of Hartman-Stampacchia theorem. J. Optim. Theory Appl. 74:445-456
3. Chen GY, Yang XQ (1990) The vector complementary problem and its equivalences with the weak minimal elements in ordered spaces. J. Math. Anal. Appl. 153(1):136-158
4. Cottle RW, Pang JS (1978) A least-element theory of solving linear complementarity problems as linear programs. Math. Oper. Res. 3(2):155-170
5. Cottle RW, Pang JS, Stone RE (1992) The Linear Complementarity Problems. Academic Press, New York
6. Cryer CW, Dempster MAH (1980) Equivalence of linear complementarity problems and linear programs in vector lattice Hilbert spaces. SIAM J. Control Optim. 18(1):76-90
7. Fang YP, Huang NJ (2003) The vector F-complementary problems with demipseudo-monotone mappings. Appl. Math. Lett. 16:1019-1024
8. Fang YP, Huang NJ Least element problems of vector feasible sets for vector F-complementarity problems with pseudomonotonicity. Acta Math. Sinica (to appear)
9. Giannessi F (1980) Theorems of Alterative, Quadratic Progams and Complementarity Problems. In: Cottle RW, Giannessi F, Lions JL (eds.) Variational Inequalities and Complementarity Problems., Wiley, New York
10. Giannessi F(ed.) (2000) Vector Variational Inequalities and Vector Equilibria. Kluwer Academic Publishers, Dordrecht
11. Harker PT, Pang JS (1990) Finite-dimensional variational and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Programming. 48:161-220
12. Isac G (1992) Complementarity Problems, Lecture Notes in Math., 1528. Springer-Verlag, Berlin
13. Konnov IV, Yao JC (1997) On the generalized vector variational inequality problem. J. Math. Anal. Appl. 206(1):42-58
14. Kum S, Lee GM (2002) Remarks on implicit vector variational inequalities. Taiwanese J. Math. 6(3):369-382
15. Mangasarian OL (1976) Linear complementarity problems solvable by a single linear program. Math. Programming. 10(2):263-270
16. Mangasarian OL (1977) Characterization of linear complementarity problems as linear programs. Math. Prog. Study 9:74-87
17. Mangasarian OL (1979) Simplified characterizations of linear complementarity problems solvable as linear programs. Math. Oper. Res. 4(3):268-273
18. Murty KG (1987) Linear Complementarity, Linear and Nonlinear Programming. Heldermann Verlag, Berlin.
19. Riddell RC (1981) Equivalence of nonlinear complementarity problems and least element problems in Banach lattices. Math. Oper. Res. 6:462-474
20. Schaible S, Yao JC (1995) On the equivalence of nonlinear complementarity problems and least element problems, Math. Programming. 70:191-200
21. Yang XQ (1993) Vector variational inequality and its duality. Nonlinear Anal. TMA 95:729-734
22. Yang XQ (1993) Vector complementarity and minimal element problems, J. Optim. Theory Appl. 77(3):483-495