Duality in Nondifferentiable Vector Programming

Osuna-Gómez, R.; Rufián-Lizana, A.; Ruı́z-Canales, P.

doi:10.1006/jmaa.2000.7417

Cited by 10 publications

(13 citation statements)

References 12 publications

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“…In other words, such a definition has the property of not involving the resolution of a multiobjective problem. Furthermore, our definition generalizes the one introduced in Osuna-Gómez et al [17] for the corresponding case, when (P) is stated in a finite-dimensional setting.…”

Section: Saddle Point Type Conditionsmentioning

confidence: 82%

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Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

Santos

Rojas-Medar

Oliveira

2012

TCAM

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Abstract. This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789-809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

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Section: Saddle Point Type Conditionsmentioning

confidence: 82%

“…Following Osuna-Gómez et al [17], we give a definition of saddle points which has the feature of being based on solving scalar problems and not vector ones, as usual. We, then, show that every point that satisfies our definition is a weakly efficient solution.…”

Section: Introduction and Formulation Of The Problemmentioning

confidence: 99%

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

Santos

Rojas-Medar

Oliveira

2012

TCAM

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“…There are some partial results to this question. See [23,26] for problems in finite dimensions and [29,30] for infinite dimensional problems. In [23], Geoffrion identifies the equivalence between the problems under convexity assumptions.…”

Section: The Scalarization Methodsmentioning

confidence: 99%

“…Osuna-Gómez et al [26] introduced a new dual problem for vector optimization problems with the special feature of being a scalar program. In this paper (see Section 6) a similar one for continuous-time problems is defined and duality theorems are proved.…”

Section: Introductionmentioning

confidence: 99%

Vector continuous-time programming without differentiability

Oliveira

2010

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this work continuous-time programming problems of vector optimization are considered. Firstly, a nonconvex generalized Gordan's transposition theorem is obtained. Then, the relationship with the associated weighting scalar problem is studied and saddle point optimality results are established. A scalar dual problem is introduced and duality theorems are given. No differentiability assumption is imposed.

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“…Yang [15] studied the nondifferentiable symmetric duality, in which the objective function contains a support function. Osuna-Gómez, Rufián-Lizana and Ruíz-Canales [11] studied the Lagrange duality in multi-objective optimization for generalized subconvex-like functions. The set-valued derivative of generalized realvalued functions was introduced and used to study minimization problems were studied by Li [9] .…”

Section: Introductionmentioning

confidence: 99%