Semidefinite Relaxation for Two Mixed Binary Quadratically Constrained Quadratic Programs: Algorithms and Approximation Bounds

This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs and analyzes their approximation performance. The first class of problems finds two minimum norm vectors in N -dimensional real or complex Euclide...

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Vydáno v:Journal of the Operations Research Society of China (Internet) Ročník 4; číslo 2; s. 205 - 221
Hlavní autoři: Xu, Zi, Hong, Ming-Yi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Beijing Operations Research Society of China 01.06.2016
Springer Nature B.V
Témata:
Algorithms
Approximation
Constraints
Continuity (mathematics)
Euclidean geometry
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Quadratic programming
Quality of service
Semidefinite programming
90C20
NP-hard
Nonconvex quadratically constrained quadratic programming
Semidefinite program relaxation
90C22
90C59
Approximation bound
ISSN:2194-668X, 2194-6698
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Shrnutí:This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs and analyzes their approximation performance. The first class of problems finds two minimum norm vectors in N -dimensional real or complex Euclidean space, such that M out of 2 M concave quadratic constraints are satisfied. By employing a special randomized rounding procedure, we show that the ratio between the norm of the optimal solution of this model and its SDP relaxation is upper bounded by 54 M 2 π in the real case and by 24 M π in the complex case. The second class of problems finds a series of minimum norm vectors subject to a set of quadratic constraints and cardinality constraints with both binary and continuous variables. We show that in this case the approximation ratio is also bounded and independent of problem dimension for both the real and the complex cases.
Bibliografie:ObjectType-Article-1
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ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-015-0082-2