Results 21 to 30 of about 549 (53)
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
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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
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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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Polynomial Optimization with Real Varieties [PDF]
, 2013 We consider the optimization problem of minimizing a polynomial f(x) subject to polynomial constraints h(x)=0, g(x)>=0. Lasserre's hierarchy is a sequence of sum of squares relaxations for finding the global minimum. Let K be the feasible set.
Nie, Jiawang
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LIBOR additive model calibration to swaptions markets [PDF]
, 2008 In the current paper, we introduce a new calibration methodology for the LIBOR market model driven by LIBOR additive processes based in an inverse problem.
Colino, Jesús P. +2 more
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Approximations of convex bodies by polytopes and by projections of spectrahedra [PDF]
, 2012 We prove that for any compact set B in R^d and for any epsilon >0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points such that the maximum absolute value of any linear function ell: R^d --> R on X approximates the maximum absolute value of ...
Barvinok, Alexander
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Exposed faces of semidefinitely representable sets
, 2009 A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite.
Netzer, Tim +2 more
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Improved bounds for the crossing numbers of K_m,n and K_n
, 2004 It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing
de Klerk, E. +4 more
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Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix [PDF]
, 2013 The positive semidefinite rank of a nonnegative $(m\times n)$-matrix~$S$ is the minimum number~$q$ such that there exist positive semidefinite $(q\times q)$-matrices $A_1,\dots,A_m$, $B_1,\dots,B_n$ such that $S(k,\ell) = \mbox{tr}(A_k^* B_\ell)$.
Dirk, Oliver Theis, Troy Lee
core
Interiors of completely positive cones [PDF]
, 2014 A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $A = BB^T$. We characterize the interior of the CP cone.
Fan, Jinyan, Zhou, Anwa
core