Invex functions and generalized convexity in multiobjective programming

Martin (Ref. 1) studied the optimality conditions of invex functions for scalar programming problems. In this work, we generalize his results making them applicable to vectorial optimization problems. We prove that the equivalence between minima and stationary points or Kuhn-Tucker points (depending...

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Bibliographic Details
Published in:Journal of optimization theory and applications 1998-09, Vol.98 (3), p.651-661
Main Authors: OSUNA-GOMEZ, R, RUFIAN-LIZANA, A, RUIZ-CANALES, P
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization. Search problems
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Summary:Martin (Ref. 1) studied the optimality conditions of invex functions for scalar programming problems. In this work, we generalize his results making them applicable to vectorial optimization problems. We prove that the equivalence between minima and stationary points or Kuhn-Tucker points (depending on the case) remains true if we optimize several objective functions instead of one objective function. To this end, we define accurately stationary points and Kuhn-Tucker optimality conditions for multiobjective programming problems. We see that the Martin results cannot be improved in mathematical programming, because the new types of generalized convexity that have appeared over the last few years do not yield any new optimality conditions for mathematical programming problems.
ISSN:0022-3239
1573-2878
DOI:10.1023/A:1022628130448