This paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a pre-specified...

Abstract. The aim of this paper is to make an attempt to justify the main results from Convex Analysis by one elegant tool, the conification method, which consists of three steps: conify, work with convex cones, deconify. It is based on the fact that the standard operations and facts (`the...

In this paper, we develop various calculus rules for general smooth matrix-valued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function -log X to study a new notion of...

__Abstract__ Current methods in the shipping industry to evaluate performance do not account for differences in fleet profiles of registries such as age, size or ship type and not for bad luck. This can lead to unfair evaluation of enforcement efforts of the international standards. Furthermore,...

The following four questions could be asked about each extremalproblem: 1. What are the conditions for an extremum of the problem (necessary, sufficient, necessary andsufficient)? 2. How to describe the evolution of sulutions if the problem is perturbed? 3. Does a solution to the problem exist...

The following four questions could be asked about each extremalproblem:1. What are the conditions for an extremum of theproblem (necessary, sufficient, necessary andsufficient)?2. How to describe the evolution of sulutions if theproblem is perturbed?3. Does a solution to the problem exist or...

We consider the classical duality operators for convex objects suchas the polar of a convex set containing the origin, the dual norm,the Fenchel-transform of a convex function and the conjugate of aconvex cone. We give a new, sharper, unified treatment of the theoryof these operators, deriving...