A class of semilocal \(E\)-preinvex functions and its applications in nonlinear programming. (English) Zbl 1235.90152
Summary: A kind of generalized convex set, called as local star-shaped \(E\)-invex set with respect to \(\eta\), is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal \(E\)-preinvex functions, which is a generalization of semi-\(E\)-preinvex functions and semilocal \(E\)-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.
MSC:
| 90C30 | Nonlinear programming |
References:
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