Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces

In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) is preordered by a not necessarily solid (and not necessarily pointed) convex cone. It is well-known that there are many examples where the ordering cone of the image space has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim is to consider Pareto-type solution concepts for such vector optimization problems based on the intrinsic core notion (a well-known generalized interiority notion). We propose a new Henig-type proper efficiency concept based on generalized dilating cones which are relatively solid (i.e., their intrinsic cores are nonempty). Using linear functionals from the dual cone of the ordering cone, we are able to characterize the sets of (weakly, properly) efficient solutions under certain generalized convexity assumptions. Toward this end, we employ separation theorems that are working in the considered setting.

Efficient Solutions of Interval Programming Problems with Inexact Parameters and Second Order Cone Constraints

In this article, a methodology is developed to solve an interval and a fractional interval programming problem by converting into a non-interval form for second order cone constraints, with the objective function and constraints being interval valued functions. We investigate the parametric and non-parametric forms of the interval valued functions along with their convexity properties. Two approaches are developed to obtain efficient and properly efficient solutions. Furthermore, the efficient solutions or Pareto optimal solutions of fractional and non-fractional programming problems over R + n ⋃ { 0 } are also discussed. The main idea of the present article is to introduce a new concept for efficiency, called efficient space, caused by the lower and upper bounds of the respective intervals of the objective function which are shown in different figures. Finally, some numerical examples are worked through to illustrate the methodology and affirm the validity of the obtained results.

Symmetric duality for Bonvex multiobjective fractional continuous time programming problems

We introduced a symmetric dual for multi objective fractional variational programs in second order. Under invexity assumptions, we established weak, strong and converse duality as well as self duality relations .We work with properly efficient solutions in strong and converse duality theorems. The weak duality theorems involves efficient solutions .