Semidefinite programming formulation

SEMIDEFINITE PROGRAMMING FORMULATIONS AND PRIMAL-DUAL INTERIOR-POINT METHODS... 

A semidefinite program may be written in two complementary formulations, which are known as the primal and dual programs. Eor convenience we define the map M that transforms any vector x) of length n into an h x h matrix M x) by creating each column of the matrix sequentially with the elements of the vector. The primal formulation of the semidefinite program may be expressed in general notation as... 

We solve the nonlinear formulation of the semidefinite program by the augmented Lagrange multiplier method for constrained nonlinear optimization [28, 29]. Consider the augmented Lagrangian function... 

The semidefinite program we are considering is formulated in terms of the symmetric matrix H and the linear subspace of symmetric matrices S. For the... 

The computational implementation of the energy minimization with respect to the 2-RDM is formulated as a semidefinite program (SDP). A SDP is a generalization of a linear program where the objective variable is kept positive semidefinite. The program is constructed by considering the minimization of the linear energy functional in Eq. (2) subject to constraints... 

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