2012•Mathematical Methods in the Applied SciencesRequires access

Higher‐order generalized invexity in variational problems

Saroj Kumar Padhan, Chandal Nahak

Abstract

We introduce higher‐order duality (Mangasarian type and Mond–Wier type) of variational problems. Under higher‐order generalized invexity assumptions on functions that compose the primal problem, higher‐order duality results (weak duality, strong duality, and converse duality) are derived for this pair of problems. Also, we establish many examples and counter‐examples to support our investigation. Copyright © 2012 John Wiley & Sons, Ltd.

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Key concepts: Duality (order theory), Converse, Mathematics, Order (exchange), Duality gap, Strong duality, Weak duality, Applied mathematics