Robustness in nonsmooth nonlinear multi-objective programming

•Defining robust efficiency for nonlinear multi-objective optimization problems.•Showing that, robust efficient solutions are proper solutions (under some assumptions).•Providing a problem for calculating a robustness radius.•Comparing the newly-defined robustness notion with two existing ones.•Char...

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Bibliographic Details
Published in:European journal of operational research Vol. 247; no. 2; pp. 370 - 378
Main Authors: Zamani, Moslem, Soleimani-damaneh, Majid, Kabgani, Alireza
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.12.2015
Elsevier Sequoia S.A
Subjects:
Clarke generalized gradient
Comparative analysis
Convex analysis
Linear programming
Mathematical functions
Mathematical problems
Multiple objective programming
Nonlinear programming
Nonsmooth optimization
Optimization techniques
Proper efficiency
Robust solution
Studies
Robust solution
Nonsmooth optimization
Proper efficiency
Multiple objective programming
Clarke generalized gradient
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•Defining robust efficiency for nonlinear multi-objective optimization problems.•Showing that, robust efficient solutions are proper solutions (under some assumptions).•Providing a problem for calculating a robustness radius.•Comparing the newly-defined robustness notion with two existing ones.•Characterizing robust solutions and studying alterations of objectives. Recently Georgiev, Luc, and Pardalos (2013), [Robust aspects of solutions in deterministic multiple objective linear programming, European Journal of Operational Research, 229(1), 29–36] introduced the notion of robust efficient solutions for linear multi-objective optimization problems. In this paper, we extend this notion to nonlinear case. It is shown that, under the compactness of the feasible set or convexity, each robust efficient solution is a proper efficient solution. Some necessary and sufficient conditions for robustness, with respect to the tangent cone and the non-ascent directions, are proved. An optimization problem for calculating a robustness radius followed by a comparison between the newly-defined robustness notion and two existing ones is presented. Moreover, some alterations of objective functions preserving weak/proper/robust efficiency are studied.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2015.06.031