Radiant Separation Theorems and Minimum-Type Subdifferentials of Calm Functions

A. Sheykhi () and A. R. Doagooei ()
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A. Sheykhi: Shahid Bahonar University of Kerman
A. R. Doagooei: Shahid Bahonar University of Kerman

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 5, 693-711

Abstract: Abstract Applying minimum-type functions and plus-cogauges, we construct a closed, convex cone in order to separate a boundary point of a radiant set from its interior. Abstract convexity of positively homogeneous functions is studied as well. Since a locally Lipschitz function is degree-one calm, the class of degree-one calm functions is large. We study degree-one calm functions and investigate how these functions can be generated by a class of min-type functions. Then, we derive a method to find an element of the subdifferential of a non-negative, lower semicontinuous and degree-one calm function with respect to the class of min-type functions.

Keywords: Global optimization; Min-type function; Abstract convexity; Radiant set; Separation theorems; Subdifferential; 26B25; 49N15; 90C46 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1132-1

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