We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms whose iteration complexity we analyse are so-called short-step algorithms. Our iteration complexity bounds match the current best iteration complexity bounds for primal-dual symmetric interior-point algorithm of Nesterov and Todd, for symmetric cone programming...

‎in this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎the proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the newton equation system‎, ‎by using an inexact newton direction‎. ‎furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone K, a logarithmically homogeneous self-concordant barrier for K and any positive real number r ≤ 1, we associate, with each direction x ∈ K, a second-order cone K̂r(x) containing K. We show that K is the intersection of the second-order cones K̂r(x), as x ranges through ...

Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has an exact symmetric nonnegative factorization, is called a completely positive tensor. This concept extends the concept of completely positive matrices. A classical result in the theory of completely positive m...

We investigate a cone in the symmetric group algebra introduced by Stembridge [2]. It is dual to the cone of monomial-positive immanants of n × n matrices with indeterminate entries. We present a new set of relations between elements of the dual cone, and use these relations to show that the cone is finitely generated for n = 6, generalizing Stembridge’s result for n = 5.

— Let g be a finite dimensional complex reductive Lie algebra and S(g) its symmetric algebra. The nilpotent bicone of g is the subset of elements (x, y) of g×g whose subspace generated by x and y is contained in the nilpotent cone. The nilpotent bicone is naturally endowed with a scheme structure, as nullvariety of the augmentation ideal of the subalgebra of S(g) ⊗C S(g) generated by the 2-orde...

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

Proper functioning of sensory systems requires the generation of appropriate numbers and proportions of neuronal subtypes that encode distinct information. Perception of color relies on signals from multiple cone photoreceptor types. In cone-dominated retinas, each cone expresses a single opsin type with peak sensitivity to UV, long (L) (red), medium (M) (green), or short (S) (blue) wavelengths...

We study the component Hn of the Hilbert scheme whose general point parameterizes a pair of codimension two linear subspaces in Pn for n ≥ 3. We show that Hn is smooth and isomorphic to the blow-up of the symmetric square of G(n−2, n) along the diagonal. Further Hn intersects only one other component in the full Hilbert scheme, transversely. We determine the stable base locus decomposition of i...

We say that a symmetric matrix A is copositive if vTAv ≥ 0 for all nonnegative vectors v. The main result of this paper is a characterization of the cone of feasible directions at a copositive matrix A, i.e., the convex cone of symmetric matrices B such that there exists δ > 0 satisfying A + δB being copositive. This cone is described by a set of linear inequalities on the elements of B constru...