Struct totsu::ProbSDP

pub struct ProbSDP<L: LinAlgEx> { /* private fields */ }

Semidefinite program

The problem is \[ \begin{array}{ll} {\rm minimize} & c^Tx \\ {\rm subject \ to} & \sum_{i=0}^{n - 1} x_i F_i + F_n \preceq 0 \\ & A x = b, \end{array} \] where

• variables \( x \in \mathbb{R}^n \)
• \( c \in \mathbb{R}^n \)
• \( F_j \in \mathcal{S}^k \) for \( j = 0, \ldots, n \)
• \( A \in \mathbb{R}^{p \times n},\ b \in \mathbb{R}^p \).

This is already a conic problem and can be reformulated as follows: \[ \begin{array}{ll} {\rm minimize} & c^Tx \\ {\rm subject \ to} & \left[ \begin{array}{ccc} {\rm vec}(F_0) & \cdots & {\rm vec}(F_{n - 1}) \\ & A & \end{array} \right] x + s = \left[ \begin{array}{c} -{\rm vec}(F_n) \\ b \end{array} \right] \\ & s \in {\rm vec}(\mathcal{S}_+^k) \times \lbrace 0 \rbrace^p. \end{array} \]

\( {\rm vec}(X) = (X_{11}\ \sqrt2 X_{12}\ X_{22}\ \sqrt2 X_{13}\ \sqrt2 X_{23}\ X_{33}\ \cdots)^T \) which extracts and scales the upper-triangular part of a symmetric matrix X in column-wise. ConePSD is used for \( {\rm vec}(\mathcal{S}_+^k) \).

Implementations

impl<L: LinAlgEx> ProbSDP<L>

pub fn new(
    vec_c: MatBuild<L>,
    syms_f: Vec<MatBuild<L>>,
    mat_a: MatBuild<L>,
    vec_b: MatBuild<L>,
    eps_zero: L::F
) -> Self

Creates a SDP with given data.

Returns a ProbSDP instance.

• vec_c is \(c\).
• syms_f is \(F_0, \ldots, F_n\) each of which shall belong to MatType::SymPack.
• mat_a is \(A\).
• vec_b is \(b\).
• eps_zero should be the same value as totsu_core::solver::SolverParam::eps_zero.

pub fn problem(
    &mut self
) -> (ProbSDPOpC<'_, L>, ProbSDPOpA<'_, L>, ProbSDPOpB<'_, L>, ProbSDPCone<'_, L>, &mut [L::F])

Generates the problem data structures to be fed to Solver::solve.

Returns a tuple of operators, a cone and a work slice.