(untitled) (Statistics, Optimization & Information Computing, 2025)
In this paper, we introduce another generalization of semilocally convex functions over cones, called conesemilocally subconvex 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 optimal solutions of the mathematical programming problem (MP) over cones using these functions, directional derivatives, and the alternative theorem. Investigation of optimal solutions of (MP) is done by deriving optimality and duality results for semilocally subconvex mathematical programming problems over cones (MP).