Non-conflicting ordering cones and vector optimization in inductive limits

Necessary Optimality Conditions for εe–Pareto Solutions in Vector Optimization with Empty Interior Ordering Cones

We present new necessary optimality conditions for εe–Pareto optimal solutions of constrained vector optimization problems with empty interior ordering cones. We use the dual-space approach based on advanced tools of variational analysis and generalized differentiation. It allows us not implement any scalarization technique while be able to establish necessary results for nonconvex and nonsolid...

Variable Ordering Structures in Vector Optimization

Second-order optimality and duality in vector optimization over cones

In this paper, we introduce the notion of a second-order coneconvex function involving second-order directional derivative. Also, second-order cone-pseudoconvex, second-order cone-quasiconvex and other related functions are defined. Second-order optimality and Mond-Weir type duality results are derived for a vector optimization problem over cones using the introduced classes of functions.

Ordering Structures in Vector Optimization and Applications in Medical Engineering

This manuscript is on the theory and numerical procedures of vector optimization w.r.t. various ordering structures, on recent developments in this area and, most important, on their application to medical engineering. In vector optimization one considers optimization problems with a vectorvalued objective map and thus one has to compare elements in a linear space. If the linear space is the fi...

Finite rank vector bundles on inductive limits of grassmannians

If P is the projective ind-space, i.e. P is the inductive limit of linear embeddings of complex projective spaces, the Barth-Van de Ven-Tyurin (BVT) Theorem claims that every finite rank vector bundle on P is isomorphic to a direct sum of line bundles. We extend this theorem to general sequences of morphisms between projective spaces by proving that, if there are infinitely many morphisms of de...