p-regular nonlinearity: tangency at singularity in degenerate optimization problems

Ewa M. Bednarczuk () and Alexey Tretyakov
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Ewa M. Bednarczuk: Systems Research Institute
Alexey Tretyakov: Faculty of Sciences

Mathematical Methods of Operations Research, 2017, vol. 86, issue 3, No 4, 485-500

Abstract: Abstract We investigate description of the tangent cone to the null set of a mapping F at a given point $$x^{*}$$ x ∗ in the case when F is degenerate at $$x^{*}$$ x ∗ . To this aim we introduce the concept of modified 2-regular mappings, which generalizes the concept of p-regular mappings. Our main result provides the description of the tangent cone to the null set of modified 2-regular mappings. With the help of this result we derive new optimality conditions for a wide class of optimization problems with equality constraints.

Keywords: Tangent cone; Degenerate mapping; p-regularity; Nonlinear optimization problems; Optimality conditions; 46N10; 47J30; 47N10; 90C30 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-017-0611-3

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