Proper efficiency conditions and duality for multiobjective programming problems involving semilocally invex functions

Das, Laxminarayan; Nanda, Sudarsan

doi:10.1080/02331939508844092

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2011

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Cited by 10 publications

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“…Subsequently, Egudo [4] and Weir [9] proved duality results for a differentiable multiobjective program with pseudoconvex/quasiconvex functions. Das and Nanda [3] have studied the duality theorems of Mond-Weir type for a multiobjective programming problem with semilocally invex functions. Xu [10] has studied mixed-type duality in multiobjective programming problems.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective duality withρ − (η, θ)‐invexity

Nahak

Nanda

2005

International Journal of Stochastic Analysis

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Section: Introductionmentioning

confidence: 99%

Multiobjective duality withρ − (η, θ)‐invexity

Nahak

Nanda

2005

International Journal of Stochastic Analysis

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Nonlinear Multiobjective Programming

Engau

2011

Wiley Encyclopedia of Operations Research and Management Science

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This introductory treatment of the theory and methodology of nonlinear multiobjective programming offers an annotated bibliographic overview of various concepts and approaches to solve continuous deterministic multicriteria optimization problems. First, the notions of Pareto optimality, efficiency, and nondominance are discussed and then related to approximate, epsilon, and proper efficiency. Second, after highlighting similarities and pointing out differences to first‐ and second‐order optimality conditions in classical nonlinear programming, several other topics including duality and sensitivity are also mentioned. Third, a number of solution approaches and generating methods are described with a particular focus on scalarizations using objective aggregation, prioritization, and norm or distance minimization to some utopian reference point.

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