Nonsmooth Invexity in Multiobjective Programming

Abstract In this paper, we extend Reiland’s results for a nonlinear (single objective) optimization problem involving nonsmooth Lipschitz functions to a nonlinear multiobjective optimization problem (MP). The Kuhn-Tucker optimality theorems and the duality theorems for (MP) are obtained.

[1]  On generalized pseudoconvex functions , 1989 .

[2]  Jean-Baptiste Hiriart-Urruty,et al.  On optimality conditions in nondifferentiable programming , 1978, Math. Program..

[3]  M. A. Hanson On sufficiency of the Kuhn-Tucker conditions , 1981 .

[4]  S. Nanda,et al.  Generalised convexity and symmetric duality in nonlinear programming , 1990 .

[5]  B. M. Glover,et al.  Invex functions and duality , 1985, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[6]  Adi Ben-Israel,et al.  What is invexity? , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[7]  M. A. Hanson,et al.  Multiobjective duality with invexity , 1987 .

[8]  P. Wolfe A duality theorem for non-linear programming , 1961 .