Self-dual convex cones arise, for example, in the study of copositive matrices and copositive quadratic forms. We begin by giving necessary and sufficient conditions for a cone to be the orthogonal transform of the positive orthant. Next we give a technique for constructing self-dual cones in ...
Cite this conference paper Quantum Fields — Algebras, Processes J. Bellissard& B. Iochum 171Accesses Abstract It is shown that the category of homogeneous self-dual cones in Hilbert spaces is isomorphic to the category of Jordan Banach algebras with predual (JBW-algebras). ...
Geometry of homogeneous convex cones, duality mapping, and optimal self-concordant barriers We study homogeneous convex cones. We first characterize the extreme rays of such cones in the context of their primal construction (due to Vinberg) and al......
Let K be a closed convex cone with dual in a finite-dimensional real inner-product space V. The complementarity set of K is We say that a linear transforma... M Orlitzky - 《Optimization Methods & Software》 被引量: 0发表: 2017年 Forthcoming in Mathematical Programming CONIC MIXED-INTEGER...
Convex Pr o gr amming: The ory and A lgorithms. SIAM Publications. SIAM, Philadelphia, USA, 1994. [6] Y u. E. Nestero v and M. J. T o dd. Self-scaled barriers and in terior-p oin t metho ds for con v ex programming. Mathematics of Op er ations R ese ar ch, 22:1{42...
Convex OptimizationConvex ConeConic OptimizationDualityLevel SetsSelf-Dual EmbeddingSelf-scaled ConeThere is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measSocial Science Electronic Publishing...
The aim of the present note is twofold: to give a geometric characterization of the closed convex sets which are invariant with respect to these operations, and to relate this invariance property to the isotonicity of the metric projection onto these sets. As concrete examples the Lorentz cone ...
An irreducible homogeneous non-selfdual cone of arbitrary rank linearly isomorphic to the dual coneIn this note we present an irreducible homogeneous non-selfdual open convex cone of arbitrary rank r (r ≥ 3) that is linearly isomorphic to the dual cone. 2009 by World Scientific Publishing Co...
AN IRREDUCIBLE HOMOGENEOUS NON-SELFDUAL CONE OF ARBITRARY RANK LINEARLY ISOMORPHIC TO THE DUAL CONEhomogeneous open convex coneIn this note we present an irreducible homogeneous non-selfdual open convex cone of arbitrary rank r (r > 3) that is linearly isomorphic to the dual cone....
S.: Conic convex programming and self-dual embedding - Luo, Sturn, et al. - 2000 () Citation Context ... and also [5] for additional information.) (ii) If A is affine and B is the cone of positive semidefinite matrices, then the gap between A and B need not be realized at a ...