Necessary and sufficient second order optimality conditions for multiobjective problems with C1 data

L. B. Santos; R. Osuna-Gómez; B. Hernández-Jiménez; M. A. Rojas-Medar

doi:10.1016/j.na.2013.02.020

Necessary and sufficient second order optimality conditions for multiobjective problems with C¹ data

L. B. Santos
, R. Osuna-Gómez
, B. Hernández-Jiménez
, M. A. Rojas-Medar

Universidade Tecnológica Federal do Paraná
University of Seville
Universidad Pablo de Olavide
Universidad del Bío-Bío

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency.

Original language	English
Pages (from-to)	192-203
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	85
DOIs	https://doi.org/10.1016/j.na.2013.02.020
State	Published - 2013
Externally published	Yes

Keywords

Multiple objective programming Generalized convexity Optimality conditions

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10.1016/j.na.2013.02.020

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abstract = "In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency.",

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language = "English",

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AU - Santos, L. B.

AU - Osuna-Gómez, R.

AU - Hernández-Jiménez, B.

AU - Rojas-Medar, M. A.

PY - 2013

Y1 - 2013

N2 - In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency.

AB - In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency.

KW - Multiple objective programming Generalized convexity Optimality conditions

UR - https://www.scopus.com/pages/publications/84875744864

U2 - 10.1016/j.na.2013.02.020

DO - 10.1016/j.na.2013.02.020

M3 - Article

AN - SCOPUS:84875744864

SN - 0362-546X

VL - 85

SP - 192

EP - 203

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

Necessary and sufficient second order optimality conditions for multiobjective problems with C¹ data

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Keywords

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