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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Vydáno v:	European journal of operational research Ročník 247; číslo 2; s. 370 - 378
Hlavní autoři:	Zamani, Moslem, Soleimani-damaneh, Majid, Kabgani, Alireza
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.12.2015 Elsevier Sequoia S.A
Témata:	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
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Abstract	•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.
AbstractList	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. •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.
Author	Zamani, Moslem Soleimani-damaneh, Majid Kabgani, Alireza
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Cites_doi	10.1007/BF00934353 10.1016/j.ejor.2013.02.037 10.1137/080734510 10.1016/0022-247X(68)90201-1 10.1016/j.ejor.2014.03.013 10.1007/s001860000043 10.1023/B:COAP.0000018877.86161.8b 10.1016/j.ejor.2013.10.028 10.1162/evco.2006.14.4.463 10.1137/0315004 10.1016/j.ejor.2014.10.027
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SubjectTerms	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
Title	Robustness in nonsmooth nonlinear multi-objective programming
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