In general nonlinear programming problems to find a solution which minimizes an objective function under given constraints, one whose objective function and constraint region are convex is called a convex programming problem. For such convex programming problems, there have been proposed many efficient solution method as the successive quadratic programming method and the general gradient metho...

Report The aim of this work is to make some investigations concerning duality for mul-tiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, unde...

Abstract: In this paper, we generalize the (V, ρ)-invexity defined for nonsmooth multiobjective fractional programming by Mishra, Rueda and Giorgi (2003) to variational programming problems by defining new classes of vector-valued functions called (V, ρ)B-type I and generalized (V, ρ)-B-type I. Then we use these new classes to derive various sufficient optimality conditions and mixed type duali...

In this paper, a generalization of convexity, namely Gf-invexity is considered. We formulate Mond-Weir type symmetric dual for class nondifferentiable multiobjective fractional programming problem over cones. Next, we prove appropriate duality results using assumptions.

A multiobjective programming algorithm may find multiple nondominated solutions. If these solutions are scattered more uniformly over the Pareto frontier in the objective space, they are more different choices and hence their quality is better. In this paper, we propose a quality measure called U-measure to measure the uniformity of a given set of nondominated solutions over the Pareto frontier...

In this paper new results are established in multiobjective DC programming with infinite convex constraints (MOPIC for abbr.) that are defined on Banach space (finite or infinite) with objectives given as the difference of convex functions subject to infinite convex constraints. This problem can also be called multiobjective DC semi-infinite and infinite programming, where decision variables ru...

whereAn is the n-fold product of the σ-algebraA of subsets of a given set X ,Fi,Gi, i∈ p ≡ {1,2, . . . , p}, and Hj , j ∈ q, are real-valued functions defined on An, and for each i ∈ p, Gi(S) > 0 for all S∈An such that Hj(S) 0, j ∈ q. This paper is essentially a continuation of the investigation that was initiated in the companion paper [6] where some information about multiobjective fractional...

In this paper we study fuzzy multiobjective optimization problems defined for $n$ variables.  Based on a new $p$-dimensional fuzzy stationary-point definition,  necessary  efficiency conditions are obtained.  And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.

In this paper, we deal with multiobjective integer programming problems involving random variable coefficients in objective functions and/or constraints. After reformulation of them on the basis of a probability maximization model for the chance constrained programming, incorporating fuzzy goals of the decision maker for the objective functions, we propose an interactive fuzzy satisficing metho...