Optimizing completely positive maps using semidefinite programming
نویسندگان
چکیده
منابع مشابه
Optimizing a polyhedral-semidefinite relaxation of completely positive programs
It has recently been shown (Burer, Math Program 120:479–495, 2009) that a large class of NP-hard nonconvex quadratic programs (NQPs) can be modeled as so-called completely positive programs, i.e., the minimization of a linear function over the convex cone of completely positive matrices subject to linear constraints. Such convex programs are NP-hard in general. A basic tractable relaxation is g...
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An n×n matrix X is called completely positive semidefinite (cpsd) if there exist d×d Hermitian positive semidefinite matrices {Pi}i=1 (for some d ≥ 1) such that Xij = Tr(PiPj), for all i, j ∈ {1, . . . , n}. The cpsd-rank of a cpsd matrix is the smallest d ≥ 1 for which such a representation is possible. In this work we initiate the study of the cpsd-rank which we motivate twofold. First, the c...
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A real symmetric matrix M is completely positive semidefinite if it admits a Gram representation by positive semidefinite matrices (of any size d). The smallest such d is called the completely positive semidefinite rank of M , and it is an open question whether there exists an upper bound on this number as a function of the matrix size. We show that if such an upper bound exists, it has to be a...
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This paper is concerned with completely positive and semidefinite relaxations of quadratic programs with linear constraints and binary variables as presented in Burer [2]. It observes that all constraints of the relaxation associated with linear constraints of the original problem can be accumulated in a single linear constraint without changing the feasible set of either the completely positiv...
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Gluings of completely positive maps (CPMs) are defined and investigated. As a brief description of this concept consider a pair of ‘evolution machines’, each with the ability to evolve the internal state of a ‘particle’ inserted into its input. Each of these machines is characterized by a channel describing the operation the internal state has experienced when the particle is returned at the ou...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2002
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.65.030302