Generalized convex functions: properties, optimality and duality
R. N. Kaul, Surjeet Kaur · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1984
It is shown that a set which is closed and locally star shaped at each of its points is convex. Moreover, a semilocally convex function on a closed set which is also lower semi-continuous is a convex function. A characterization is given for a function to be semilocally convex. For a nonlinear programming problem involving semilocally convex functions, a dual is associated and necessary optimality conditions derived.