# Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition using ϵ-constraint method

RAIRO - Operations Research - Recherche Opérationnelle (2014)

- Volume: 48, Issue: 4, page 429-453
- ISSN: 0399-0559

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topOjha, A. K., and Ota, Rashmi Ranjan. "Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition using ϵ-constraint method." RAIRO - Operations Research - Recherche Opérationnelle 48.4 (2014): 429-453. <http://eudml.org/doc/275036>.

@article{Ojha2014,

abstract = {Optimization is an important tool widely used in formulation of the mathematical model and design of various decision making problems related to the science and engineering. Generally, the real world problems are occurring in the form of multi-criteria and multi-choice with certain constraints. There is no such single optimal solution exist which could optimize all the objective functions simultaneously. In this paper, ϵ-constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used to solve multi-objective Geometric programming problems(MOGPP) for searching a compromise solution. To find the suitable compromise solution for multi-objective Geometric programming problems, a brief solution procedure using ϵ-constraint method has been presented. The basic concept and classical principle of multi-objective optimization problems with KKT condition has been discussed. The result obtained by ϵ-constraint method with help of KKT condition has been compared with the result so obtained by Fuzzy programming method. Illustrative examples are presented to demonstrate the correctness of proposed model.},

author = {Ojha, A. K., Ota, Rashmi Ranjan},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {geometric programming; Karush-Kuhn-Tucker (KKT) condition; ϵ-constraint method; fuzzy programming; duality theorem; Pareto optimal solution; -constraint method},

language = {eng},

number = {4},

pages = {429-453},

publisher = {EDP-Sciences},

title = {Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition using ϵ-constraint method},

url = {http://eudml.org/doc/275036},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Ojha, A. K.

AU - Ota, Rashmi Ranjan

TI - Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition using ϵ-constraint method

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 4

SP - 429

EP - 453

AB - Optimization is an important tool widely used in formulation of the mathematical model and design of various decision making problems related to the science and engineering. Generally, the real world problems are occurring in the form of multi-criteria and multi-choice with certain constraints. There is no such single optimal solution exist which could optimize all the objective functions simultaneously. In this paper, ϵ-constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used to solve multi-objective Geometric programming problems(MOGPP) for searching a compromise solution. To find the suitable compromise solution for multi-objective Geometric programming problems, a brief solution procedure using ϵ-constraint method has been presented. The basic concept and classical principle of multi-objective optimization problems with KKT condition has been discussed. The result obtained by ϵ-constraint method with help of KKT condition has been compared with the result so obtained by Fuzzy programming method. Illustrative examples are presented to demonstrate the correctness of proposed model.

LA - eng

KW - geometric programming; Karush-Kuhn-Tucker (KKT) condition; ϵ-constraint method; fuzzy programming; duality theorem; Pareto optimal solution; -constraint method

UR - http://eudml.org/doc/275036

ER -

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