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Approximation of the Stability Number of a Graph via Copositive Programming
TLDR
This paper shows how the stability number can be computed as the solution of a conic linear program (LP) over the cone of copositive matrices of a graph by solving semidefinite programs (SDPs) of increasing size (lift-and-project method).
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Aspects of semidefinite programming : interior point algorithms and selected applications
TLDR
The Primal Logarithmic Barrier Method and Primal-Dual Affine-Scaling Methods are presented, as well as some alternative methods for reducing the number of coefficients in a graph, using the Lovasz upsilon function.
SIAM Journal on Optimization
The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear…
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Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming
TLDR
This paper shows how to approximate the optimal solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more refined, linear matrix inequalities (LMI's).
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Aspects of Semidefinite Programming
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Reduction of symmetric semidefinite programs using the regular $$\ast$$-representation
TLDR
A general technique to reduce the size ofSemidefinite programming problems on which a permutation group is acting is described, based on a low-order matrix based on the representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices.
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Global optimization of rational functions: a semidefinite programming approach
TLDR
It is shown that in the univariate case (n = 1), these problems have exact reformulations as semidefinite programming (SDP) problems, by using reformulations introduced in the PhD thesis of Jibetean [16].
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Error Bounds for Some Semidefinite Programming Approaches to Polynomial Minimization on the Hypercube
We consider the problem of minimizing a polynomial on the hypercube $[0,1]^n$ and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to…
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A PTAS for the minimization of polynomials of fixed degree over the simplex
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Improved Bounds for the Crossing Numbers of Km, n and Kn
TLDR
Improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values are shown, obtained as a consequence of the new bound on $\Cr(\ksn) 2.1796n^2 - 4.5n".
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