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Mathematical Methods of Operations Research

, Volume 55, Issue 3, pp 347–358 | Cite as

On general vector quasi-optimization problems

  • Angelo Guerraggio
  • Nguyen Xuan Tan
Article

Abstract

Vector general quasi-optimization problems are formulated and some sufficient conditions on the existence of solutions for these problems are shown. These concern the existence of solutions, the stability and the structure of solution set of general vector problems. As special case, we obtain results on the existence of solutions of vector quasi-optimization problem. Some relationships between these problems and others, as vector quasi-equilibrium problems, quasi-variational inequalities, complementarity problems,..., are shown. From these we extend some well-known results obtained by Blum and Oettli [4], Park [21], Chan and Pang [6], Parida and Sen [20], Browder and Minty [18], Fan [8], etc.

Key words: General quasi-optimization problem Vector optimization problem Quasi-equilibrium problem Upper and lower C-convex multivalued mappings Strictly C-quasiconvex and Properly C-quasiconvex multivalued mappings Upper and lower C-continuous multi-valued mappings 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Angelo Guerraggio
    • 1
  • Nguyen Xuan Tan
    • 2
  1. 1.Università Bocconi, I.M.Q., v.le Isonzo 25, 20135 Milano, Italia (e-mail: angelo.guerraggio@uni-bocconi.it)IT
  2. 2.Hanoi University, Institute of Mathematics, P.O. Box 631, Bo Ho 10000, Hanoi, VietnamVN

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