Mathematical programming with Semilocally Subconvex functions over cones

In this paper, we introduce another generalization of semilocally convex functions over cones, called conesemilocallysubconvex function (C-slsb), and compare it with other generalizations of convex functions through examples.Further, using its properties we establish a theorem of the alternatives fo...

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Bibliographic Details
Published in:	Statistics, optimization & information computing Vol. 14; no. 3; pp. 1473 - 1480
Main Authors:	Sharma, Vani, Chaudhary, Mamta, Grover, Meetu Bhatia
Format:	Journal Article
Language:	English
Published:	02.09.2025
ISSN:	2311-004X, 2310-5070
Online Access:	Get full text
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Summary:	In this paper, we introduce another generalization of semilocally convex functions over cones, called conesemilocallysubconvex function (C-slsb), and compare it with other generalizations of convex functions through examples.Further, using its properties we establish a theorem of the alternatives for these functions. Then we investigate the optimalsolutions of the mathematical programming problem (MP) over cones using these functions, directional derivatives, andthe alternative theorem. Investigation of optimal solutions of (MP) is done by deriving optimality and duality results forsemilocally subconvex mathematical programming problems over cones (MP).
ISSN:	2311-004X 2310-5070
DOI:	10.19139/soic-2310-5070-2502