Generalization of preinvex and B-vex functions. (English) Zbl 0802.49026

Summary: A class of functions called \(B\)-preinvex functions is introduced by relaxing the definitions of preinvex and \(B\)-vex functions. Examples are given to show that there exist functions which are \(B\)-preinvex but not preinvex or \(B\)-vex or quasipreinvex. Some of the properties of \(B\)-invex functions are obtained.


49M37 Numerical methods based on nonlinear programming
49J52 Nonsmooth analysis
49K27 Optimality conditions for problems in abstract spaces
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