OPTIMALITY CONDITIONS IN SUB-(b, m)-CONVEX PROGRAMMING

By modulating the definitions of m-convex functions and sub-b-convex functions, the authors introduce a new class of generalized convex functions called sub-(b; m)-convex functions and derive some basic properties for the newly introduced functions. Furthermore, The sufficient conditions of optimality for both unconstrained and inequality constrained sub-(b; m)-convex programming are presented. Also some optimality conditions of nonlinear multi-objective sub-(b; m)-convex programming are established.