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Duality in nonlinear programming

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Abstract

In this paper are defined new first- and second-order duals of the nonlinear programming problem with inequality constraints. We introduce a notion of a WD-invex problem. We prove weak, strong, converse, strict converse duality, and other theorems under the hypothesis that the problem is WD-invex. We obtain that a problem with inequality constraints is WD-invex if and only if weak duality holds between the primal and dual problems. We introduce a notion of a second-order WD-invex problem with inequality constraints. The class of WD-invex problems is strictly included in the class of second-order ones. We derive that the first-order duality results are satisfied in the second-order case.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Varna, 1 Studentska Str., 9010, Varna, Bulgaria

    Vsevolod I. Ivanov

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  1. Vsevolod I. Ivanov
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Correspondence to Vsevolod I. Ivanov.

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Ivanov, V.I. Duality in nonlinear programming. Optim Lett 7, 1643–1658 (2013). https://doi.org/10.1007/s11590-012-0512-6

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  • DOI: https://doi.org/10.1007/s11590-012-0512-6

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