Semi-prequasi-invex type multiobjective optimization and generalized fractional programming problems

In this paper, we mainly discuss some applications of semi-prequasi-invex type functions for multiobjective optimization and generalized nonlinear programming problems. Some optimality results for semi- prequasi-invex type multiobjective optimization problem are given, then some optimality necessary conditions under directional derivative and saddle point theories in semi-prequasi-invex type nonlinear programming problem are derived. Moreover, some duality theorems for the generalized nonlinear fractional programming problem with semi-prequasi-invexity are also obtained. Our results improve the corresponding ones in the literature.