Efficiency and proper efficiency in nonlinear vector maximization problems

A nonlinear vector maximum problem (NLVMP) is considered. An equivalent vector maximum problem (VMP) is formulated by linearizing the objectives of NLVMP. Assuming generalized convexity and a constraint qualification, necessary and sufficient conditions in both Kuhn-Tucker and Isermann form are obtained for an efficient solution of NLVMP. Also, if objectives are pseudolinear and satisfy a certain boundedness condition, it is proved that every efficient solution of NLVMP is properly efficient. Finally, a numerical example is discussed to illustrate the results.