Semilocal E-Convexity And Its Applications

Convexity and generalized convexity play a key role in many aspects of optimization theories, such as optimality conditions, saddle-point theorems, duality theorems, theorems of alternatives, and convergence of optimization algorithms, so the research on convexity and generalized convexity has been one of the important aspects in mathematical programming.In this paper, a new type of generalized convexity—semilocal E-convexity is introduced, and some of its basic characters are studied, some optimality conditions and duality theorems for the associated generalized convex programming are discussed. Furthermore, some optimality conditions and duality results are also obtained for the fractional multiple objective programming problem involving semilocal E-convex functions and related functions.