Abstarct: The conventional equilibria problem found in many economics and network models is based on a scalar cost, or a single objective. Recently, equilibria problems based on a vector cost, or multicriteria, have received considerable attention. In this paper, we study a scalarization method for analyzing network equilibria problems with vector-valued cost function. The method is based on th...

We propose a vector optimization approach to linear Cournot oligopolistic market equilibrium models where the strategy sets depend on each other. We use scalarization technique to find a Pareto efficient solution to the model by using a jointly constrained bilinear programming formulation. We then propose a decomposition branch-and-bound algorithm for globally solving the resulting bilinear pro...

Optimization is an important tool in computational finance and business intelligence. Multiple criteria mathematical program(MCMP), which is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously, is one of the ways of utilizing optimization techniques. Due to the existence of multiple objectives, MCMPs are usually difficult t...

This paper presents a new method for the numerical solution of nonlinear multiobjective optimization problems with an arbitrary partial ordering in the objective space induced by a closed pointed convex cone. This algorithm is based on the well-known scalarization approach by Pascoletti and Serafini and adaptively controls the scalarization parameters using new sensitivity results. The computed...

We present a proximal point method to solve multiobjective problems based on the scalarization for maps. We build a family of a convex scalar strict representation of a convex map F with respect to the lexicographic order on R and we add a variant of the logarithmquadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced on the quadratic term and ...

In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the concept of multivariate conditional ...

Abstract Robust optimization is proving to be a fruitful tool study problems with uncertain data. In this paper we deal the minmax aproach robust multiobjective optimization. We survey main features of problem particular reference results concerning linear scalarization and sensitivity optimal values respect changes in uncertainty set. Furthermore prove solutions Finally apply presented mean-va...

Every TVS-cone metric space is topologically isomorphic to a topological metric space. In this paper, by using a nonlinear scalarization, we give some fixed point results with nonlinear contractive conditions on TVS-cone metric spaces.