Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization
نویسندگان
چکیده
منابع مشابه
Simplified semidefinite and completely positive relaxations
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...
متن کاملCompletely Positive Semidefinite Rank
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...
متن کاملCompletely positive reformulations for polynomial optimization
Polynomial optimization encompasses a very rich class of problems in which both the objective and constraints can be written in terms of polynomials on the decision variables. There is a well established body of research on quadratic polynomial optimization problems based on reformulations of the original problem as a conic program over the cone of completely positive matrices, or its conic dua...
متن کاملMatrices with High Completely Positive Semidefinite Rank
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...
متن کاملExtension of Completely Positive Cone Relaxation to Polynomial Optimization
We propose the moment cone relaxation for a class of polynomial optimization problems (POPs) to extend the results on the completely positive cone programming relaxation for the quadratic optimization (QOP) model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the POPs, so that efficient numerical methods can be developed in the future. We es...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Global Optimization
سال: 2017
ISSN: 0925-5001,1573-2916
DOI: 10.1007/s10898-017-0558-1