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

Authors

  • Lucelina Batista dos Santos Universidade Federal do Paraná
  • Marko Antonio Rojas-Medar Universidad del Bío-Bío - Campus Fernando May
  • Valeriano Antunes de Oliveira Universidade Estadual Paulista - Campus de São José do Rio Preto

DOI:

https://doi.org/10.5540/tema.2012.013.02.0179

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.

Author Biographies

Lucelina Batista dos Santos, Universidade Federal do Paraná

Centro Politécnico - Setor de Ciências Exatas - Departamento de Matemática

Marko Antonio Rojas-Medar, Universidad del Bío-Bío - Campus Fernando May

Facultad de Ciencias - Departamento de Ciencias Básicas - Grupo de Matemática Aplicada

Valeriano Antunes de Oliveira, Universidade Estadual Paulista - Campus de São José do Rio Preto

Instituto de Biociências, Letras e Ciências Exatas - Departamento de Ciências de Computação e Estatística

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Published

2012-08-31

How to Cite

dos Santos, L. B., Rojas-Medar, M. A., & de Oliveira, V. A. (2012). Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization. Trends in Computational and Applied Mathematics, 13(2), 179–191. https://doi.org/10.5540/tema.2012.013.02.0179

Issue

Vol. 13 No. 2 (2012)

Section

Original Article

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