Wolfe duality and MondWeir duality via perturbations

Radu Ioan Boţ; Sorin Mihai Grad

doi:10.1016/j.na.2010.03.026

Wolfe duality and MondWeir duality via perturbations

Radu Ioan Boţ
, Sorin Mihai Grad

Fac. Math. of the TU

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

Abstract

Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and MondWeir duals, respectively, follow as particularizations of the general duals by using the Lagrange perturbation. Examples to show the differences between the new duals are given and a gate towards other generalized convexities is opened.

Original language	English
Pages (from-to)	374-384
Number of pages	11
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	73
Issue number	2
DOIs	https://doi.org/10.1016/j.na.2010.03.026
Publication status	Published - 15 Jul 2010
Externally published	Yes

Keywords

Conjugate functions
Convex subdifferentials
MondWeir duality
Regularity conditions
Wolfe duality

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10.1016/j.na.2010.03.026

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abstract = "Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and MondWeir duals, respectively, follow as particularizations of the general duals by using the Lagrange perturbation. Examples to show the differences between the new duals are given and a gate towards other generalized convexities is opened.",

keywords = "Conjugate functions, Convex subdifferentials, MondWeir duality, Regularity conditions, Wolfe duality",

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AU - Boţ, Radu Ioan

AU - Grad, Sorin Mihai

PY - 2010/7/15

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N2 - Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and MondWeir duals, respectively, follow as particularizations of the general duals by using the Lagrange perturbation. Examples to show the differences between the new duals are given and a gate towards other generalized convexities is opened.

AB - Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and MondWeir duals, respectively, follow as particularizations of the general duals by using the Lagrange perturbation. Examples to show the differences between the new duals are given and a gate towards other generalized convexities is opened.

KW - Conjugate functions

KW - Convex subdifferentials

KW - MondWeir duality

KW - Regularity conditions

KW - Wolfe duality

UR - https://www.scopus.com/pages/publications/77955426608

U2 - 10.1016/j.na.2010.03.026

DO - 10.1016/j.na.2010.03.026

M3 - Article

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VL - 73

SP - 374

EP - 384

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 2

ER -

Wolfe duality and MondWeir duality via perturbations

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