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• W2000640794 abstract "Convexity plays a very important role in optimization for establishing optimality conditions. Different works have shown that the convexity property can be replaced by a weaker notion, the invexity. In particular, for problems with inequality-type constraints, Martin defined a weaker notion of invexity, the Karush–Kuhn–Tucker-invexity (hereafter KKT-invexity), that is both necessary and sufficient to obtain Karush–Kuhn–Tucker-type optimality conditions. It is well known that for this result to hold the problem has to verify a constraint qualification, i.e., it must be regular or non-degenerate. In non-regular problems, the classical optimality conditions are totally inapplicable. Meaningful results were obtained for problems with inequality-type constraints by Izmailov. They are based on the 2-regularity condition of the constraints at a feasible point. In this work, we generalize Martin's result to non-regular problems by defining an analogous concept, the 2-KKT-invexity, and using the characterization of the tangent cone in the 2-regular case and the necessary optimality condition given by Izmailov." @default.
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• W2000640794 date "2009-04-01" @default.
• W2000640794 modified "2023-10-18" @default.
• W2000640794 title "Generalized convexity in non-regular programming problems with inequality-type constraints" @default.
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• W2000640794 doi "https://doi.org/10.1016/j.jmaa.2008.11.013" @default.
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