The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform

Alberto Seeger - One of the best experts on this subject based on the ideXlab platform.

  • Cone-Constrained Eigenvalue Problems: Structure of Cone Spectra
    Set-Valued and Variational Analysis, 2021
    Co-Authors: Alberto Seeger
    Abstract:

    There is a rich literature devoted to the eigenvalue analysis of variational inequalities. Of special interest is the case in which the constraint set of the variational inequality is a Closed Convex Cone. The set of eigenvalues of a matrix A relative to a Closed Convex Cone K is called the K -spectrum of A . Cardinality and topological results for Cone spectra depend on the kind of matrices and Cones that are used as ingredients. It is important to distinguish for instance between symmetric and nonsymmetric matrices and, on the other hand, between polyhedral and nonpolyhedral Cones. However, more subtle subdivisions are necessary for having a better understanding of the structure of Cone spectra. This work elaborates on this issue.

  • Centers of sets with symmetry or cyclicity properties
    TOP, 2013
    Co-Authors: Alberto Seeger, Mounir Torki
    Abstract:

    We introduce an axiomatic formalism for the concept of the center of a set in a Euclidean space. Then we explain how to exploit possible symmetries and possible cyclicities in the set in order to localize its center. Special attention is paid to the determination of centers in Cones of matrices. Despite its highly abstract flavor, our work has a strong connection with Convex optimization theory. In fact, computing the so-called “incenter” of a solid Closed Convex Cone is a matter of solving a nonsmooth Convex optimization program. On the other hand, the concept of the incenter of a solid Closed Convex Cone has a bearing on the complexity analysis and design of algorithms for Convex optimization programs under conic constraints.

  • Aperture angle analysis for ellipsoids.
    Electronic Journal of Linear Algebra, 2013
    Co-Authors: Alberto Seeger
    Abstract:

    Let Ω ⊆ R n be a compact Convex set and x be a point in the exterior of Ω. The aperture angle of x relative to Ω is defined as the maximal angle of the smallest Closed Convex Cone that contains Ω − x. This note provides an explicit formula, based on eigenvalues of symmetric matrices, for the aperture angle of a point relative to an ellipsoid.

  • Solidity indices for Convex Cones.
    Positivity, 2012
    Co-Authors: Daniel Gourion, Alberto Seeger
    Abstract:

    The issue addressed in this work is how to measure the degree of solidity of a Closed Convex Cone in the Euclidean space R n. One compares and establishes all sort of relations between the metric, the volumetric, and the Frobenius solidity indices.

  • Condition number and eccentricity of a Closed Convex Cone
    MATHEMATICA SCANDINAVICA, 2011
    Co-Authors: René Henrion, Alberto Seeger
    Abstract:

    We discuss some extremality issues concerning the circumradius, the inradius, and the condition number of a Closed Convex Cone in $\mathsf{R}^n$. The condition number refers to the ratio between the circumradius and the inradius. We also study the eccentricity of a Closed Convex Cone, which is a coefficient that measures to which extent the circumcenter differs from the incenter.

S. Sundar - One of the best experts on this subject based on the ideXlab platform.

  • CCR flows associated to Closed Convex Cones
    arXiv: Operator Algebras, 2019
    Co-Authors: Anbu Arjunan, S. Sundar
    Abstract:

    Let $P$ be a Closed Convex Cone in $\mathbb{R}^{d}$ which we assume to be spanning and pointed i.e. $P-P=\mathbb{R}^{d}$ and $P \cap -P=\{0\}$. In this article, we consider CCR flows over $P$ associated to isometric representations that arises out of $P$-invariant Closed subsets, also called as $P$-modules, of $\mathbb{R}^{d}$. We show that for two $P$-modules the associated CCR flows are cocycle conjugate if and only if the modules are translates of each other.

  • On the existence of E0-semigroups — the multiparameter case
    Infinite Dimensional Analysis Quantum Probability and Related Topics, 2018
    Co-Authors: S. P. Murugan, S. Sundar
    Abstract:

    Let P ⊂ ℝd be a Closed Convex Cone. Assume that P is pointed, i.e. the intersection P ∩−P = {0} and P is spanning, i.e. P − P = ℝd. Denote the interior of P by Ω. Let E be a product system over Ω. ...

  • On the Wiener-Hopf compactification of a Symmetric Cone
    arXiv: Operator Algebras, 2016
    Co-Authors: S. Sundar
    Abstract:

    Let V be a finite dimensional real Euclidean Jordan algebra with the identity element 1. Let Q be the Closed Convex Cone of squares. We show that the Wiener- Hopf compactification of Q is the interval (1-Q) \cap (-1+Q). As a consequence, we deduce that the K-groups of the Wiener-Hopf C^{*}-algebra associated to Q are trivial.

Jen-chih Yao - One of the best experts on this subject based on the ideXlab platform.

  • Viscosity-type Approximation Method for Efficient Solutions in Vector Optimization
    Taiwanese Journal of Mathematics, 2010
    Co-Authors: Thai Doan Chuong, Jen-chih Yao
    Abstract:

    The paper is devoted to developing the viscosity-type approximation algorithm of finding efficient solutions to the vector optimization problem for a mapping between finite dimensional Hilbert spaces with respect to the partial order induced by a pointed Closed Convex Cone. We prove that under some suitable conditions either the sequence generated by our method converges to an efficient solution or its cluster points belong to the set of all efficient solutions of this problem.

  • NONEXPANSIVE RETRACTIONS ONTO Closed Convex ConeS IN BANACH SPACES
    Taiwanese Journal of Mathematics, 2010
    Co-Authors: Takashi Honda, Wataru Takahashi, Jen-chih Yao
    Abstract:

    Let $E$ be a smooth, strictly Convex and reflexive Banach space, let $C^*$ be a Closed Convex subset of the dual space $E^*$ of $E$ and let $\Pi_{C^*}$ be the generalized projection of $E^*$ onto $C^*$. Then the mapping $R_{C^*}$ defined by $R_{C^*}=J^{-1}\Pi_{C^*}J$ is a sunny generalized nonexpansive retraction of $E$ onto $J^{-1}C^{*}$, where $J$ is the normalized duality mapping on $E$. In this paper, we first prove that if $K$ is a Closed Convex Cone in $E$ and $P$ is the nonexpansive retaction of $E$ onto $K$, then $P$ a sunny generalized nonexpansive retraction of $E$ onto $K$. Using this result, we obtain an equivalent condition for a Closed half-space of $E$ to be a nonexpansive retract of $E$.

  • Pseudo-monotone complementarity problems in Hilbert space
    Journal of Optimization Theory and Applications, 1992
    Co-Authors: Richard W. Cottle, Jen-chih Yao
    Abstract:

    In this paper, some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over an arbitrary Closed Convex Cone in a real Hilbert space are established. In particular, some known existence results for a nonlinear complementarity problem in a finite-dimensional Hilbert space are generalized to an infinite-dimensional real Hilbert space. Applications to a class of nonlinear complementarity problems and the study of the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions are given.

Stefan Tappe - One of the best experts on this subject based on the ideXlab platform.

Tappe Stefan - One of the best experts on this subject based on the ideXlab platform.