Optim Lett DOI 10.1007/s11590-013-0661-2 ORIGINAL PAPER Modified objective function method in nonsmooth vector optimization over cones S. K. Suneja · Sunila Sharma · Malti Kapoor Received: 24 March 2012 / Accepted: 23 May 2013 © Springer-Verlag Berlin Heidelberg 2013 Abstract In this paper optimality for a nonsmooth vector optimization problem hav- ing generalized cone-invex objective and constraint functions is considered. An equiv- alent η-approximated vector optimization problem is constructed by a modification of the objective function. The relationships between weakly efficient solutions and saddle points of the two problems are studied. Keywords Cone-invex functions · Lagrange function · KKT-conditions · Nonsmooth vector optimization · Weakly efficient solutions 1 Introduction Vector optimization or multiobjective programming deals with the optimization of several incommensurable objectives to the best possible extent. The study of multi- objective programming has wide applications in various fields of economics, decision theory, game theory, information theory and optimal control theory. Due to the various conflicting objectives involved in a multiobjective program, no single solution usually optimizes all of them at the same time. In this quest for solutions of a multiobjective program, Antczak [1, 2] devised the η-approximation method for solving a differen- tiable non-linear multiobjective program involving invex functions. He established the equivalence between the weakly efficient solutions of the original problem and its modified objective function problem under the conditions of invexity/generalized S. K. Suneja · S. Sharma Department of Mathematics, Miranda House, University of Delhi, Delhi 110007, India M. Kapoor (B ) Department of Mathematics, Motilal Nehru College (M), University of Delhi, Delhi 110021, India e-mail: maltikapoor1@gmail.com; malti_dumaths@rediffmail.com 123