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Second-Order Cone Problems (SOCP)
\mathbf{f^T x \to min}
subjected to
\mathbf{lb \le x \le ub}
\mathbf{A} \mathbf{x} \le \mathbf{b}
\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}
\mathbf{\forall i = 0,\dots,I: \lVert C_i x + d_i \rVert_2 \leq q_i^T x + s_i}
 x,\ f \in \mathbb{R}^n
C_i \in \mathbb{R}^{{m_i}\times n}, \ d_i \in \mathbb{R}^{m_i}
q_i \in \mathbb{R}^n, \ s_i \in \mathbb{R}
A_{eq} \in \mathbb{R}^{p_{eq}\times n}, \ b_{eq} \in \mathbb{R}^{p_{eq}}

Attentionattention: OO versions <= 0.31 has bug with handling lb and ub



SOCP solvers connected to OpenOpt:

Solver License Info
cvxopt_socp GPL3 requires CVXOPT installation
FuturePlans: mosek, cplex commercial

See also:

  • wikipedia.org SOCP entry
  • one of recent SOCP benchmarks by Hans Mittelmann (2008-Nov-11)
  • QP, SDP, MIQP, QCQP, MIQCQP
Retrieved from "http://openopt.org/SOCP"
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