Differential and sensitivity properties of gap functions for vector variational inequalities

Mathematical Methods of Operations Research

Volumn 57, Issue 3, 2003, Pages 377-391

  Li, S J ^a,b   Yan, Hong ^b   Chen, G Y ^c  

^a CHONGQING UNIVERSITY   (China)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^c INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Contingent derivative; Gap function; Vector variational inequalities

Indexed keywords

MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; OPTIMIZATION; PROBLEM SOLVING; SENSITIVITY ANALYSIS; VECTORS;

CONTIGENT DERIVATIVE; GAP FUNCTION; VECTOR OPTIMIZATION; VECTOR VARIATIONAL INEQUALITIES;

FUNCTIONS;

EID: 21244446300     PISSN: 14322994     EISSN: 14325217     Source Type: Journal    
DOI: 10.1007/s001860200254     Document Type: Article

References (16)

1. Aubin JP, Ekeland I (1984) Applied nonlinear analysis. John Wiley & Sons, New York
2. Aubin JP, Frankowska H (1990) Set-valued analysis. Birkhauser, Boston
3. Auslender (1976) A optimisation: Methods numeriques. Masson Paris
4. Chen GY (1992) Existence of solutions for a vector variational inequality: An extension of hartman-stampacchia theorem. Journal of Optimization Theory and Applications 74:445-456
5. Chen GY, Goh CJ, Yang XQ (2000) On gap functions for vector variational inequalities. In: Giannessi F (ed.) Vector Variational Inequality and Vector Equilibria. Mathematical Theories, Kluwer Academic Publishers, Boston, pp. 55-70
6. Daniele P, Maugeri A (2000) Vector variational inequalities and modeling of a continuum traffic equilibrium problem. In: Giannessi F (ed.) Vector Variational Inequality and Vector Equilibria. Mathematical Theories, Kluwer Academic Publishers, Boston, pp. 97-109
7. Daniilidis A, Hadjisaws N (1996) Existence theorem for vector variational inequalities. Bulletin of Australia Mathematical Society 54:473-481
8. Dauer JP, Saleh OA (1993) A characterization of proper minimal points as solutions of sublinear optimization problems 178:227-246
9. Giannessi F (1980) Theorems of alternative, quadratic programs and complementarity problems. In: Cottle RW, Giannessi F, Lions JL (eds) Variational Inequalities and Complementarity Problems, John Wiley & Sons, Chichester, England pp. 151-186
10. Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory. Algorithms and Applications, Mathematical Programming 48:161-220
11. Konnov V, Yao JC (1997) On the generalized vector variational inequality problem. Journal of Mathematical Analysis and Applications 206:42-58
12. Lee GM, Kim DS, Lee BS (1998) Vector variational inequality as a tool for studying vector optimization problems. Nonlinear Analysis, Theory Method & Applications 34:745-765
13. Li SJ, Chen GY, Lee GM (2000) Minimax theorems for set-valued mappings. Journal of Optimization Theory and Applications 106:183-200
14. Shi DS (1991) Contingent derivative of the perturbation map in multiobjective optimization. Journal of Optimization Theory and Applications 70:385-396
15. Tanino T (1988) Sensitivity analysis in multiobjective optimization. Journal of Optimization Theory and Applications 56:479-499
16. Tanino T (1988) Stability and sensitivity analysis in convex vector optimization. SIAM Journal on Control and Optimization 26:512-536