SDP

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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 Aeqx = beq. Can handle parameters gaptol (default 1e-5), iprint and maxIter (integers, from prob structure).

See also:

  • SOCP, QP, QCQP, MIQP, MIQCQP
  • wikipedia.org SDP entry
  • Semidefinite Programming portal (by Christoph Helmberg)
  • one of recent SDP benchmarks by Hans MittelmannSDP (10 Apr 2008)
Retrieved from "http://openopt.org/SDP"
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