SDP

Semidefinite Problems (SDP)

$\mathbf{f^T x \to min}$

subjected to

$\mathbf{lb \le x \le ub}$

$\mathbf{A x \le b}$

$\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}$

$\mathbf{\forall i = 0,...,I: \sum_{j=0}^{n-1} S^{ij} x_j \le d^i}$

(matrix componentwise inequalities)

$\mathbf{x \in R^n;\ S^{ij}, d^i \in R^{m_i \times m_i}}$

$\mathbf{i = 0,...,I;\ j = 0,...,n-1}$

$\mathbf{S^{ij}}$ are positive semidefinite matrices

SDP solvers connected to OpenOpt:

Solver	License	Info
cvxopt_sdp	LGPL	requires CVXOPT installed. Can handle iprint = -1, 0 or 1
dsdp	GPL	requires CVXOPT + DSDP installation (latter is performed automatically provided you use Linux apt-get), can't handle linear equality constraints $A e q x = b e q$ . Can handle parameters gaptol (default 1e-5), iprint and maxIter (integers, from prob structure).

See also: