A variational principle for vector equilibrium problems

  • K. R. Kazmi


A variational principle is described and analysed for the solutions of vector equilibrium problems.


Vector equlibrium problem variational principle P-convexity P - ψ-monotonicity 


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  1. [A]
    Auchmuty G, Variational principles for variational inequalities,Numer. Funct. Anal. Optim. 10 (1989) 863–874CrossRefMathSciNetMATHGoogle Scholar
  2. [B-O1]
    Blum E and Oettli W, Variational principles for equilibrium problems, parametric optimization and related topics, III (Güstrow 1991), in: Approximation and Optimization (eds) J Guddat, H Th Jongen, B Kummer and F Nozieka (Lang, Frankfurt am Main)3 (1993) 79–88Google Scholar
  3. [B-O2]
    Blum E and Oettli W, From optimization and variational inequalities to equilibrium problems,Math. Stud. 63 (1994) 123–145MATHMathSciNetGoogle Scholar
  4. [C]
    Chen G-Y, Existence of solution of vector variational inequality: An extension of the Hartmann-Stampacchia theorem,J. Optim. Theory Appl. 74 (1992) 445–456MATHCrossRefMathSciNetGoogle Scholar
  5. [C-C]
    Chen G-Y and Craven B D, Existence and continuity of solutions for vector optimization,J. Optim. Theory Appl. 81 (1994) 459–468MATHCrossRefMathSciNetGoogle Scholar
  6. [H-P]
    Harker P T and Pang J-S, Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications,Math. Prog. B48 (1990) 161–220CrossRefMathSciNetGoogle Scholar
  7. [K1]
    Kazmi K R, Some remarks on vector optimization problems,J. Optim. Theory Appl. 96 (1998) 133–138MATHCrossRefMathSciNetGoogle Scholar
  8. [K2]
    Kazmi K R, On vector equilibrium problem,Proc. Indian Acad. Sci. (Math.Sci.) 110 (2000) 213–223MATHMathSciNetCrossRefGoogle Scholar
  9. [K3]
    Kazmi K R, Existence of solutions for vector saddle-point problems, in: Vector variational inequalities and vector equilibria, Mathematical Theories (ed) F Giannessi (Kluwer Academic Publishers, Dordrecht, Netherlands) (2000) 267–275Google Scholar
  10. [K-A]
    Kazmi K R and Ahmad K, Nonconvex mappings and vector variational-like inequalities, in: Industrial and Applied Mathematics (eds) A H Siddiqi and K Ahmad (New Delhi, London: Narosa Publishing House) (1998) 103–115Google Scholar
  11. [Y]
    Yang X-Q, Vector complementarity and minimal element problems,J. Optim. Theory Appl. 77 (1993) 483–495MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Printed in India 2001

Authors and Affiliations

  • K. R. Kazmi
    • 1
  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia

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