Struct totsu::ProbQP

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

Quadratic program

The problem is \[ \begin{array}{ll} {\rm minimize} & {1 \over 2} x^T P x + q^T x + r \\ {\rm subject \ to} & G x \preceq h \\ & A x = b, \end{array} \] where

• variables \( x \in \mathbb{R}^n \)
• \( P \in \mathcal{S}_{+}^n,\ q \in \mathbb{R}^n,\ r \in \mathbb{R} \)
• \( G \in \mathbb{R}^{m \times n},\ h \in \mathbb{R}^m \)
• \( A \in \mathbb{R}^{p \times n},\ b \in \mathbb{R}^p \).

In the following, \( r \) does not appear since it does not matter.

The representation as a conic linear program is as follows: \[ \begin{array}{ll} {\rm minimize} & t \\ {\rm subject \ to} & \left[ \begin{array}{ccc} 0 & 0 \\ q^T & -1 \\ -P^{1 \over 2} & 0 \\ G & 0 \\ A & 0 \end{array} \right] \left[ \begin{array}{c} x \\ t \end{array} \right] + s = \left[ \begin{array}{c} 1 \\ 0 \\ 0 \\ h \\ b \end{array} \right] \\ & s \in \mathcal{Q}_r^{2 + n} \times \mathbb{R}_+^m \times \lbrace 0 \rbrace^p. \end{array} \]

\( \mathcal{Q}_r \) is a rotated second-order (or quadratic) cone (see ConeRotSOC).

Implementations

impl<L: LinAlgEx> ProbQP<L>

pub fn new(
    sym_p: MatBuild<L>,
    vec_q: MatBuild<L>,
    mat_g: MatBuild<L>,
    vec_h: MatBuild<L>,
    mat_a: MatBuild<L>,
    vec_b: MatBuild<L>,
    eps_zero: L::F
) -> Self

Creates a QP with given data.

Returns the ProbQP instance.

• sym_p is \(P\) which shall belong to totsu_core::MatType::SymPack.
• vec_q is \(q\).
• mat_g is \(G\).
• vec_h is \(h\).
• 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
) -> (ProbQPOpC<L>, ProbQPOpA<'_, L>, ProbQPOpB<'_, L>, ProbQPCone<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.