socp#

swordfish.function.socp()#

Solve SOCP problems and calculate the minimum of the objective function under specified constraints. The standard form of the SOCP constraint is as follows:

\[\begin{split}\begin{align*} \text{minimize}\quad & f^T x\\ \text{subject to}\quad & \|A_i x + b_i\|_2 \le c_i^T x + d_i,\quad i=1,\dots,m,\\ & A x = b \end{align*}\end{split}\]

G is as follows:

\[\begin{align*} \big[ -c_0 \;|\; -A_0^{T} \;|\; \dots \;|\; -c_i \;|\; -A_i^{T} \;|\; \dots \big]^{T} \end{align*}\]

h is as follows:

\[\begin{align*} [d_0 \mid b_0 \mid \dots \mid d_i \mid b_i \mid \dots]^{T} \end{align*}\]
Parameters:

  • f (Constant) – A numeric vector indicating the coefficient vector of the objective function.

  • G (Constant, optional) – A numeric matrix indicating the coefficient matrix of the cone constraint, by default DFLT.

  • h (Constant, optional) – A numeric vector indicating the right-hand-side vector of the cone constraint, by default DFLT.

  • l (Constant, optional) – An integral scalar indicating the dimension of the non-negative quadrant constraint, by default DFLT.

  • q (Constant, optional) – A positive vector indicating the dimension size of each second-order cone constraint. The form is [r0,r1,…,rN-1], by default DFLT.

  • A (Constant, optional) – A numeric matrix indicating the coefficient matrix of the equality constraint, by default DFLT.

  • b (Constant, optional) – A numeric vector indicating the right-hand-side vector of the equality constraint, by default DFLT.

Returns:

A 3-element tuple:

  • The first element is a string indicating the state of the solution:

    • Problem solved to optimality: optimal solution found;

    • Found certificate of primal infeasibility: no feasible solution to the primal;

    • Found certificate of dual infeasibility: no feasible solution to the dual;

    • Offset exitflag at inaccurate results: inaccurate results;

    • Maximum number of iterations reached: reach the maximum number of iterations;

    • Search direction unreliable: unreliable search direction;

    • Unknown problem in solver: the solver cannot identify the problem.

  • The second element is the value of x where the value of the objective function is minimized.

  • The third element is the minimum value of the objective function.

Return type:

Constant

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