Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize)
over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron.[1]
Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be modeled or approximated as semidefinite programming problems. In automatic control theory, SDPs are used in the context of linear matrix inequalities. SDPs are in fact a special case of cone programming and can be efficiently solved by interior point methods.
All linear programs and (convex) quadratic programs can be expressed as SDPs, and via hierarchies of SDPs the solutions of polynomial optimization problems can be approximated. Semidefinite programming has been used in the optimization of complex systems. In recent years, some quantum query complexity problems have been formulated in terms of semidefinite programs.
^Gärtner, Bernd; Matoušek, Jiří (2012), Gärtner, Bernd; Matousek, Jiri (eds.), "Semidefinite Programming", Approximation Algorithms and Semidefinite Programming, Berlin, Heidelberg: Springer, pp. 15–25, doi:10.1007/978-3-642-22015-9_2, ISBN 978-3-642-22015-9, retrieved 2023-12-31
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Semidefiniteprogramming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified...
(1997). "An exact duality theory for semidefiniteprogramming and its complexity implications". Mathematical Programming. 77: 129–162. doi:10.1007/BF02614433...
known classes of convex optimization problems, namely linear and semidefiniteprogramming. Given a real vector space X, a convex, real-valued function f...
(2019-02-04). "Exact semidefinite formulations for a class of (random and non-random) nonconvex quadratic programs". Mathematical Programming. 181: 1–17. arXiv:1802...
Unfolding (MVU), also known as Semidefinite Embedding (SDE), is an algorithm in computer science that uses semidefiniteprogramming to perform non-linear dimensionality...
a convex quadratic function. Second order cone programming are more general. Semidefiniteprogramming are more general. Conic optimization are even more...
channels. Although the diamond norm can be efficiently computed via semidefiniteprogramming, it is in general difficult to obtain analytical expressions and...
penalized matrix decomposition framework, a convex relaxation/semidefiniteprogramming framework, a generalized power method framework an alternating...
^{\operatorname {T} }N\mathbf {x} \geq 0.} This property guarantees that semidefiniteprogramming problems converge to a globally optimal solution. The positive-definiteness...
stopping problems Oriented matroid Quadratic programming, a superset of linear programmingSemidefiniteprogramming Shadow price Simplex algorithm, used to...
L. E.; Jordan, M. I. (2004). "Learning the kernel matrix with semidefiniteprogramming". Journal of Machine Learning Research. 5: 27–72 [p. 29]. Horn...
approximation ratio is a method by Goemans and Williamson using semidefiniteprogramming and randomized rounding that achieves an approximation ratio α...
optimization problems, and the first to make a systematic study of semidefiniteprogramming (SDP). Also in this book, they introduced the self-concordant functions...
for k-nearest neighbor classification. The algorithm is based on semidefiniteprogramming, a sub-class of convex optimization. The goal of supervised learning...
popular relaxations include the following. Linear programming relaxations Semidefiniteprogramming relaxations Primal-dual methods Dual fitting Embedding...
Ramana, Motakuri; Goldman, A. J. (1995), "Some geometric results in semidefiniteprogramming", Journal of Global Optimization, 7 (1): 33–50, CiteSeerX 10.1...
maximum clique in polynomial time, using an algorithm based on semidefiniteprogramming. However, this method is complex and non-combinatorial, and specialized...
The solution method for semidefiniteprograms, used by this algorithm, is based on the ellipsoid method for linear programming. It leads to a polynomial...
journal requires |journal= (help) So, Anthony Man-Cho (2007). A SemidefiniteProgramming Approach to the Graph Realization Problem: Theory, Applications...
technique for casting this problem as a semidefiniteprogramming problem. Unfortunately, semidefiniteprogramming solvers have a high computational cost...
Nemirovski. Semidefiniteprogramming Spectrahedron Finsler's lemma Y. Nesterov and A. Nemirovsky, Interior Point Polynomial Methods in Convex Programming. SIAM...
level mode of certain generations of Intel's mobile processors Semidefiniteprogramming, an optimization procedure Service data point, a node in mobile...
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