An algorithm for finding the whole efficient set of a multiobjective linear program is proposed. From the set of efficient edges incident to a vertex, a characterization of maximal efficient faces containing the vertex is given. By means of the lexieographic selection rule of Dantzig, Orden and Wolfe, a connectedness property of the set of dual optimal bases associated to a degenerate vertex is...

The current state of the art for linear optimization in Flux Balance Analysis has been limited to single objective functions. Since mammalian systems perform various functions, a multiobjective approach is needed when seeking optimal flux distributions in these systems. In most of the available multiobjective optimization methods, there is a lack of understanding of when to use a particular obj...

For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints‎, ‎we define a new gap function that generalizes the definitions of this concept in other articles‎. ‎Then‎, ‎we characterize the efficient‎, ‎weakly efficient‎, ‎and properly efficient solutions of the problem utilizing this new gap function‎. ‎Our results are based on $(Phi,rho)-$invexity‎,...

This paper deals with a nonlinear multiobjective semi-infinite programming problem involving generalized (C,α, ρ, d)-convex functions. We obtain sufficient optimality conditions and formulate the Mond-Weirtype dual model for the nonlinear multiobjective semi-infinite programming problem. We also establish weak, strong and strict converse duality theorems relating the problem and the dual problem.

In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient soluti...

Two major approaches to deal with randomness or impression involved in mathematical programming problems have been developed. The one is called stochastic programming, and the other is called fuzzy programming. In this paper, we focus on multiobjective integer programming problems involving random variable coefficients in constraints. Using the concept of simple recourse, such multiobjective st...