Semidefinite programs and combinatorial optimization
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چکیده
7 Constraint generation and quadratic inequalities 29 7.1 Example: the stable set polytope again . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.2 Strong insolvability of quadratic equations . . . . . . . . . . . . . . . . . . . . . . . . 30 7.3 Inference rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 7.4 Algorithmic aspects of inference rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
منابع مشابه
Approximating Semidefinite Packing Programs
In this paper we define semidefinite packing programs and describe an algorithm to approximately solve these problems. Semidefinite packing programs arise in many applications such as semidefinite programming relaxations for combinatorial optimization problems, sparse principal component analysis, and sparse variance unfolding techniques for dimension reduction. Our algorithm exploits the struc...
متن کاملSemidefinite programs and combinatorial optimization
4 Obtaining semidefinite programs 20 4.1 Unit distance graphs and orthogonal representations . . . . . . . . . . . . . . . . . . 20 4.2 Discrete linear and quadratic programs . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.3 Spectra of graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.4 Engineering applications . . . . . . . . . . . . . . . . . . ....
متن کاملSemidefinite programs and combinatorial optimization
7 Constraint generation and quadratic inequalities 29 7.1 Example: the stable set polytope again . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.2 Strong insolvability of quadratic equations . . . . . . . . . . . . . . . . . . . . . . . . 30 7.3 Inference rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 7.4 Algorithmic aspects of inference rules . ...
متن کاملSemidefinite Programming
In semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Such a constraint is nonlinear and nonsmooth, but convex, so semidefinite programs are convex optimization problems. Semidefinite programming unifies several standard problems (e.g., linear and quadratic programming) and finds many app...
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We present a dual-scaling interior-point algorithm and show how it exploits the structure and sparsity of some large scale problems. We solve the positive semideenite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the rst computational results of interior-point algorithms for approximating the maximum cut semideenite programs with dimen...
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