Results 1 to 10 of about 567 (69)
Semidefinite bounds for nonbinary codes based on quadruples. [PDF]
Des Codes Cryptogr, 2017 For nonnegative integers $q,n,d$, let $A_q(n,d)$ denote the maximum cardinality of a code of length $n$ over an alphabet $[q]$ with $q$ letters and with minimum distance at least $d$. We consider the following upper bound on $A_q(n,d)$. For any $k$, let $
Litjens B, Polak S, Schrijver A.
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Logarithmic Barrier Method Via Minorant Function for Linear Semidefinite Programming
Annales Mathematicae Silesianae, 2023 We propose in this study, a new logarithmic barrier approach to solve linear semidefinite programming problem. We are interested in computation of the direction by Newton’s method and of the displacement step using minorant functions instead of line ...
Leulmi Assma
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EURO Journal on Computational Optimization, 2021 A conic optimization problem is a problem involving a constraint that the optimization variable be in some closed convex cone. Prominent examples are linear programs (LP), second order cone programs (SOCP), semidefinite problems (SDP), and copositive ...
Mirjam Dür, Franz Rendl
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Alternative SDP and SOCP approximations for polynomial optimization
EURO Journal on Computational Optimization, 2019 In theory, hierarchies of semidefinite programming (SDP) relaxations based on sum of squares (SOS) polynomials have been shown to provide arbitrarily close approximations for a general polynomial optimization problem (POP).
Xiaolong Kuang +3 more
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A bounded degree SOS hierarchy for polynomial optimization
EURO Journal on Computational Optimization, 2017 We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem (P):f∗=min{f(x):x∈K} on a compact basic semi-algebraic set K⊂Rn.
JeanB. Lasserre +2 more
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Improving the linear relaxation of maximum k-cut with semidefinite-based constraints
EURO Journal on Computational Optimization, 2019 We consider the maximum k-cut problem that involves partitioning the vertex set of a graph into k subsets such that the sum of the weights of the edges joining vertices in different subsets is maximized.
VilmarJefté Rodrigues de Sousa +2 more
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Upper bounds for packings of spheres of several radii
Forum of Mathematics, Sigma, 2014 We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds for packings of
DAVID DE LAAT +2 more
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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 +3 more
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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
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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
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