Given a closed convex cone P with nonempty interior in a locally convex vector space, and a set A ⊂ Y , we provide various equivalences to the implication A ∩ (−int P ) = ∅ =⇒ co(A) ∩ (−int P ) = ∅, among them, to the pointedness of cone(A + int P ). This allows us to establish an optimal alternative theorem, suitable for vector optimization problems. In addition, we characterize the two-dimens...

This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent to multiobjective optimization problems with a variable domination structure. Moreover, we introduce a nonlinear function based on a well-known nonlinear scalarization function. We...

This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the...

This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the...

The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary ...

We apply a flexible Inexact-Restoration (IR) algorithm to optimization problems with multiobjective constraints under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. We show that with the IR framework there is a natural way to explor...

We define the quasi-minimal elements of a set with respect to a convex cone and characterize them via linear scalarization. Then we attach to a general vector optimization problem a dual vector optimization problem with respect to quasi-efficient solutions and establish new duality results. By considering particular cases of the primal vector optimization problem we derive vector dual problems ...