FIRST AND SECOND ORDER SUFFICIENT CONDITIONS FOR STRICT MINIMALITY IN MULTIOBJECTIVE PROGRAMMING

In this paper, first and second order sufficient conditions are established for strict local Pareto minima of orders 1 and 2 to multiobjective optimization problems with an arbitrary feasible set and a twice differentiable objective function are provided. For this aim, the concept of support functio...

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Bibliographic Details
Published in:	Numerical functional analysis and optimization Vol. 23; no. 3-4; pp. 303 - 322
Main Authors:	Jiménez, Bienvenido, Novo, Vicente
Format:	Journal Article
Language:	English
Published:	Taylor & Francis Group 09.01.2002
Subjects:	First and second order sufficient optimality conditions Mathematics Subject Classification 2000 Multiobjective programming Primary: 90C29 Secondary: 90C46 Strict local Pareto minimum Support function
ISSN:	0163-0563, 1532-2467
Online Access:	Get full text
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Summary:	In this paper, first and second order sufficient conditions are established for strict local Pareto minima of orders 1 and 2 to multiobjective optimization problems with an arbitrary feasible set and a twice differentiable objective function are provided. For this aim, the concept of support function to a multiobjective problem is introduced, so that the scalar case in particular is contained. The obtained results generalize the classical ones of this case. Furthermore, particularizing to a feasible set defined by equality and inequality constraints, first and second order optimality conditions in primal form as well as dual form (by means of a Lagrange multiplier rule) are obtained.
ISSN:	0163-0563 1532-2467
DOI:	10.1081/NFA-120006695