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

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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.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Facultad de Ciencias Sociales y de la Comunicación, Universidad de Cádiz, Campus de Jerez de la Frontera, 11405 , Cádiz, Spain

    G. Ruiz-Garzón

  2. Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, 41012 , Sevilla, Spain

    R. Osuna-Gómez & A. Rufián-Lizana

  3. Departamento de Economía, Métodos Cuantitativos e H. Económica, Universidad Pablo de Olavide, 41013 , Sevilla, Spain

    B. Hernández-Jiménez

Authors
  1. G. Ruiz-Garzón
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  2. R. Osuna-Gómez
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  3. A. Rufián-Lizana
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  4. B. Hernández-Jiménez
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Corresponding author

Correspondence to G. Ruiz-Garzón.

Additional information

This work is supported partly by the Grant MTM2010-15383-Spain.

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Ruiz-Garzón, G., Osuna-Gómez, R., Rufián-Lizana, A. et al. Optimality in continuous-time multiobjective optimization and vector variational-like inequalities. TOP 23, 198–219 (2015). https://doi.org/10.1007/s11750-014-0334-z

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  • DOI: https://doi.org/10.1007/s11750-014-0334-z

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