A logarithmic-quadratic proximal point scalarization method for multiobjective programming

Gregório, Ronaldo Malheiros; Oliveira, Paulo Roberto

doi:10.1007/s10898-010-9544-6

Cited by 13 publications

(14 citation statements)

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“…When F is convex in (1), Bonnel at al. [5] have been proved the convergence of the proximal point method for a weak Pareto solution of the problem (1) in a general context, see also Villacorta and Oliveira [31] using proximal distances and Gregório and Oliveira [11] using a logarithmic quadratic proximal scalarization method.…”

Section: Introductionmentioning

confidence: 98%

A scalarization proximal point method for quasiconvex multiobjective minimization

2015

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In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions.We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for the non convex case, of the inexact proximal method for multiobjective convex minimization problems studied by Bonnel et al. (SIAM Journal on Optimization 15, 4, 953-970, 2005).

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Section: Introductionmentioning

confidence: 98%

A scalarization proximal point method for quasiconvex multiobjective minimization

2015

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“…Todavia, a indução de uma medida de distância de Bregman ou entrópica difere substancialmente a de Auslender e a de Gregório e Oliveira [4], pois a proposta do integrado mescla ponderadamente as características de ambas medidas de distância para qualquer α ∈ [0, 1].…”

Section: Método De Reescalamento Não-linear Integradounclassified

“…Apresentamos uma nova função ψ cujo conjugado convexoé a função logarítmica-quadrática, a qualé variante a de Auslender [1]. Entretanto, a medida de distância difere-se substancialmente a de Auslender e de Gregório e Oliveira [4]. Nós apresentamos uma abordagem primal-dual de reescalamento não-linear integrado no sentido de Griva e Polyak [3] com estratégia previsor-corretor proposta por Pinheiro [9].…”

Section: Introductionunclassified

Um método de reescalamento não-linear integrado

Pinheiro¹,

Lage²,

Silva³

et al. 2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. Neste trabalho, propomos um método de reescalamento não-linear integrado, o qual mescla as famílias de funções penalidades não-quadráticas desenvolvidas por Polyak e Teboulle [11] e Matioli e Gonzaga [7] para os métodos de lagrangiano aumentado. Além disso, definimos uma nova função para ser usada como penalidade para as restrições de desigualdade e uma abordagem primal-dual do tipo previsor-corretor. Aplicamos o método proposto no problema de fluxo de potenciaótimo reativo, da engenharia elétrica, ao sistema elétrico de 118 barras.Palavras-chave. Método de reescalamento não-linear, função lagrangiana aumentada, distâncias de Bragman e entrópicas, método dual de ponto proximal, fluxo de potênciá otimo reativo.

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“…Other authors have proposed variants of the algorithm considered by Bonnel, Iusem, and Svaiter [7] for convex vector or multiobjective problems; see, for instance, Ceng and Yao [11], Ceng, Mordukhovich, and Yao [12], Choung, Mordukhovich, and Yao [13], Gregório and Oliveira [31], and Villacorta and Oliveira [52]. Recently, the R m + -quasi-convex case was discussed in Bento, Cruz Neto, and Soubeyran [4] and Apolinário, Papa Quiroz, and Oliveira [1]; see the definition of R m + -quasi-convexity on section 2.…”

Section: Introductionmentioning

confidence: 99%

The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem

Bento¹,

Neto²,

López-Acedo³

et al. 2018

SIAM J. Optim.

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This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel, Iusem, and Svaiter [SIAM J. Optim., 15 (2005), pp. 953-970] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) approach for convergence analysis of the method is proposed where the first-order optimality condition of the scalarized problem is replaced by a necessary condition for weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.

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A logarithmic-quadratic proximal point scalarization method for multiobjective programming

Abstract: Proximal point algorithm, Scalar representations, Multiobjective programming,

Cited by 13 publications

References 5 publications

A scalarization proximal point method for quasiconvex multiobjective minimization

A scalarization proximal point method for quasiconvex multiobjective minimization

Um método de reescalamento não-linear integrado

The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem

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