I. The central result. The grandfather of it all is the celebrated 1961 theorem of Bishop and Phelps (see [7], [8]) that the set of continuous linear functionals on a Banach space E which attain their maximum on a prescribed closed convex bounded subset X c E is norm-dense in £*. The crux of the proof lies in introducing a certain convex cone in E, associating with it a partial ordering, and ap...

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...

In this paper, we follow Kuroiwa’s set approach in set optimization, which proposes to compare values of a set-valued objective map F respect to various set order relations. We introduce a Hausdorff-type distance relative to an ordering cone between two sets in a Banach space and use it to define a directional derivative for F . We show that the distance has nice properties regarding set order ...

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

generally ordering policies are done by two methods, including fix order quantity (foq) and fix order period (fop). these methods are static and either the quantity of ordering or the procedure of ordering is fixing in throughout time horizon. in real environments, demand is varying in any period and may be considered as uncertainty. when demand is variable in any period, the traditional and st...

What is the relation between notion of Nash equilibria and Pareto-optimal points? It well known that do not need to be Pareto optimal, points equilibria. However, paper “Characterizing Computing Set Equilibria via Vector Optimization” by Feinstein Rudloff takes a deeper look at relation. shown it possible characterize set all as solutions certain vector optimization problem. This accomplished c...

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

in this paper, a mathematical method is proposed to formulate a generalized ordering problem. this model is formed as a linear optimization model in which some variables are binary. the constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. on the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...

In this paper we specify the conditions on the parameters of pairs of gOS’s under which the corresponding generalized order statistics are ordered according to usual stochastic ordering, hazard rate ordering, likelihood ratio ordering and dispersive ordering. We consider this problem in one-sample as well as two-sample problems. We show that some of the results obtained by Franco et al. ...