The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z_* = min cx subject to Ax-b \in C_Y , x \in C_X, to the more general non-conic format: (GP_d) z_* = min cx subject to Ax-b \in C_Y , x \in P, where P is any closed...

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...

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...

We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in $${\mathbb{R}^n}$$ , where each distance can be measured according to a different p-norm. We show how this problem can be expressed...

We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathbb{R}^n}$$</EquationSource> </InlineEquation> , where each distance can be measured according to a different p-norm. We show how this problem can be...</equationsource></inlineequation>