Journal of Optimization Theory and Applications

, Volume 62, Issue 3, pp 449–466 | Cite as

Strong duality for infinite-dimensional vector-valued programming problems

  • H. C. Lai
  • L. S. Yang
Contributed Papers

Abstract

LetX,Y andZ be locally convex real topological vector spaces,AX a convex subset, and letCY,EZ be cones. Letf:XZ beE-concave andg:XY beC-concave functions. We consider a concave programming problem with respect to an abstract cone and its strong dual problem as follows:
$$\begin{gathered} (P)maximize f(x), subject to x \in A, g(x) \in C, \hfill \\ (SD)minimize \left\{ {\mathop \cup \limits_{\varphi \in C^ + } \max \{ (f + \varphi \circ g)(A):E\} } \right\}, \hfill \\ \end{gathered} $$
, whereC+ denotes the set of all nonnegative continuous linear operators fromY toZ and (SD) is the strong dual problem to (P). In this paper, the authors find a necessary condition of strong saddle point for Problem (P) and establish the strong duality relationships between Problems (P) and (SD).

Key Words

Cone concavity strong maximal points dual problems strong saddlepoints pseudotangent cones 

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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • H. C. Lai
    • 1
    • 2
  • L. S. Yang
    • 3
  1. 1.Institute of MathematicsNational Tsing Hua UniversityHsinchuTaiwan, ROC
  2. 2.Department of MathematicsUniversity of IowaIowa City
  3. 3.Mathematics DivisionTaitung Normal CollegeTaitungTaiwan, ROC

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