Results 11 to 20 of about 550 (54)

THE GROTHENDIECK CONSTANT IS STRICTLY SMALLER THAN KRIVINE’S BOUND

Forum of Mathematics, Pi, 2013
The (real) Grothendieck constant ${K}_{G} $ is the infimum over those $K\in (0, \infty )$ such that for every $m, n\in \mathbb{N} $ and every $m\times n$ real matrix $({a}_{ij} )$ we have $$\begin{eqnarray*}\displaystyle \max _{\{ x_{i}\} _{i= 1}^{m} , \{
MARK BRAVERMAN, KONSTANTIN MAKARYCHEV, YURY MAKARYCHEV, ASSAF NAOR   +3 more
doaj   +1 more source

Convergence of a short‐step primal‐dual algorithm based on the Gauss‐Newton direction

Journal of Applied Mathematics, Volume 2003, Issue 10, Page 517-534, 2003., 2003
We prove the theoretical convergence of a short‐step, approximate path‐following, interior‐point primal‐dual algorithm for semidefinite programs based on the Gauss‐Newton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence for the Gauss‐Newton direction in this context.
Serge Kruk, Henry Wolkowicz
wiley   +1 more source

On global optimization with indefinite quadratics

EURO Journal on Computational Optimization, 2017
We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function.
Marcia Fampa, Jon Lee, Wendel Melo
doaj   +1 more source

A note on a matrix version of the Farkas lemma [PDF]

, 2012
A linear polyomial non-negative on the non-negativity domain of finitely many linear polynomials can be expressed as their non-negative linear combination.
Zalar, Aljaž
core   +1 more source

Correction Bounds on measures satisfying moment conditions

, 2004
The Annals of Applied Probability (2002) 12 1114 ...
Lasserre, Jean B.
core   +1 more source

Adaptive First-Order Methods for General Sparse Inverse Covariance Selection [PDF]

, 2009
In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known.
Lu, Zhaosong
core   +3 more sources

Hyperbolicity cones of elementary symmetric polynomials are spectrahedral [PDF]

, 2013
We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices.
Brändén, Petter
core   +1 more source

Spectral Polyhedra

Forum of Mathematics, Sigma
A spectral convex set is a collection of symmetric matrices whose range of eigenvalues forms a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal–Sottile–Sturmfels (2011). We study this class of convex bodies,
Raman Sanyal, James Saunderson
doaj   +1 more source

Convergence analysis of a Lasserre hierarchy of upper bounds for polynomial minimization on the sphere [PDF]

, 2019
We study the convergence rate of a hierarchy of upper bounds for polynomial minimization problems, proposed by Lasserre [SIAM J. Optim. 21(3) (2011), pp. 864-885], for the special case when the feasible set is the unit (hyper)sphere.
de Klerk, Etienne, Laurent, Monique
core   +2 more sources

Bounding the support of a measure from its marginal moments

, 2010
Given all moments of the marginals of a measure on Rn, one provides (a) explicit bounds on its support and (b), a numerical scheme to compute the smallest box that contains the support.
Lasserre, Jean
core   +2 more sources