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Higher‐order generalized invexity in variational problems
Author(s) -
Padhan S.K.,
Nahak C.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2685
Subject(s) - duality (order theory) , converse , mathematics , order (exchange) , duality gap , strong duality , weak duality , type (biology) , pure mathematics , mathematical optimization , optimization problem , geometry , ecology , finance , economics , biology
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.