fi = inf( p(x) : g(x) E 4, x E R 1, P) where S is an arbitrary convex cone in a finite dimensional space, R is a convex set, and p and g are respectively convex and S-convex (on a), were given in [lo]. These characterizations hold without any constraint qualification. They use the “minimal cone” .S’ of (P) and the cone of directions of constancy D;(S’). In the faithfully convex case these cones...

We consider maps of the family of convex bodies in Euclidean ddimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d ≥ 3, a representation theorem for such maps is given, showing that they are mixtures of certain prototypes. These prototypes are obtained by app...

in this paper, we introduce a concept of a generalized $c$-distance in ordered cone $b$-metric spaces and, by using the concept, we prove some fixed point theorems in ordered cone $b$-metric spaces. our results generalize the corresponding results obtained by y. j. cho, r. saadati, shenghua wang (y. j. cho, r. saadati, shenghua wang, common fixed point  heorems on generalized distance in ordere...

We provide a complete answer to the problem which consists in finding an unpointed convex cone lying at minimal bounded Pompeiu–Hausdorff distance from a pointed one. We give also a simple and useful characterization of the radius of pointedness of a convex cone. A corresponding characterization for the radius of solidity of a convex cone is then derived by using a duality argument. c © 2007 El...

In this paper we study a special class of convex optimization problems called conically ordered convex programs (COCP), where the feasible region is given as the level set of a vector-valued nonlinear mapping, expressed as a nonnegative combination of convex functions. The nonnegativity of the vectors is defined using a pre-described conic ordering. The new model extends the ordinary convex pro...

We study the convexity property of the set QF of arbitrage-free prices of a multiperiod financial structure F . The set of arbitrage-free prices is shown to be a convex cone under conditions on the financial stucture F that hold in particular for short lived assets. Furthermore, we provide examples of equivalent financial structures F and F ′ such that QF is a convex cone, but QF ′ is neither c...

Generalized and unified versions of coincidence or maximal element theorems of Fan, Yannelis and Prabhakar, Ha, Sessa, Tarafdar, Rim and Kim, Mehta and Sessa, Kim and Tan are obtained. Our arguments are based on our recent works on a broad class of multifunctions containing composites of acyclic maps defined on convex subsets of Hausdorff topological vector spaces.

The paper is devoted to the investigation of directional derivatives and the cone of decrease directions for convex operators on Banach spaces. We prove a condition for the existence of directional derivatives which does not assume regularity of the ordering cone K. This result is then used to prove that for continuous convex operators the cone of decrease directions can be represented in terms...

A function f is said to be cone superadditive if there exists a partition of R into a family of polyhedral convex cones such that f(z + x) + f(z + y) ≤ f(z) + f(z + x+ y) holds whenever x and y belong to the same cone in the family. This concept is useful in nonlinear integer programming in that, if the objective function is cone superadditive, the global minimality can be characterized by loca...

Based on the notion of plane asymptote, we introduce new concept cone asymptote a set in n-dimensional Euclidean space. We discuss existence and describe some families asymptotes.