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Optimality in continuous-time multiobjective optimization and vector variational-like inequalities

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  • G. Ruiz-Garzón
  • R. Osuna-Gómez
  • A. Rufián-Lizana
  • B. Hernández-Jiménez

Abstract

In this paper, we study the relationships between the Stampacchia and Minty vector variational inequalities and vector continuous-time programming problems under generalized invexity and monotonicity hypotheses. We extend the results given by other authors for the scalar case to vectorial one, and we show the equivalence of efficient and weak efficient solutions for the multiobjective continuous-time programming problem, and solutions of Stampacchia and Minty variational-like type inequality problems. Furthermore, we introduce a new concept of generalized invexity for continuous-time programming problems, namely, the Karush–Kuhn–Tucker (KKT)-pseudoinvexity-II. We prove that this new concept is a necessary and sufficient condition for a vector KKT solution to be an efficient solution for a multiobjective continuous-time programming problem. In this work, duality results for Mond–Weir type dual problems are obtained, using generalized KKT-pseudoinvexity-II. This paper gives an unified point of view for optimality results in mathematical programming or control or variational inequalities problems. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • G. Ruiz-Garzón & R. Osuna-Gómez & A. Rufián-Lizana & B. Hernández-Jiménez, 2015. "Optimality in continuous-time multiobjective optimization and vector variational-like inequalities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 198-219, April.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:1:p:198-219
    DOI: 10.1007/s11750-014-0334-z
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    References listed on IDEAS

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    1. P. Daniele & A. Maugeri & W. Oettli, 1999. "Time-Dependent Traffic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 543-555, December.
    2. S. Nobakhtian & M. R. Pouryayevali, 2008. "Optimality Criteria for Nonsmooth Continuous-Time Problems of Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 69-76, January.
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