Struct totsu_core::solver::Solver

pub struct Solver<L: LinAlg> {
    pub par: SolverParam<L::F>,
}

First-order conic linear program solver struct.

This struct abstracts a solver of a conic linear program: \[ \begin{array}{ll} {\rm minimize} & c^T x \\ {\rm subject \ to} & A x + s = b \\ & s \in \mathcal{K}, \end{array} \] where

• variables \( x \in \mathbb{R}^n,\ s \in \mathbb{R}^m \)
• \( c \in \mathbb{R}^n \) as an objective linear operator
• \( A \in \mathbb{R}^{m \times n} \) and \( b \in \mathbb{R}^m \) as constraint linear operators
• a nonempty, closed, convex cone \( \mathcal{K} \).

The solution gives optimal values of primal variables \(x\) as well as dual variables \(y\) of the dual problem: \[ \begin{array}{ll} {\rm maximize} & -b^T y \\ {\rm subject \ to} & -A^T y = c \\ & y \in \mathcal{K}^*, \end{array} \] where

• variables \( y \in \mathbb{R}^m \)
• \( \mathcal{K}^* \) is the dual cone of \( \mathcal{K} \).

Fields

par: SolverParam<L::F>

solver parameters.

Implementations

impl<L: LinAlg> Solver<L>

pub fn query_worklen(op_a_size: (usize, usize)) -> usize

Query of a length of work slice.

Returns a length of work slice that Solver::solve requires.

• op_a_size is a number of rows and columns of \(A\).

pub fn new() -> Self

Creates an instance.

Returns Solver instance.

pub fn par<P>(self, f: P) -> Selfwhere
    P: FnOnce(&mut SolverParam<L::F>),

Changes solver parameters.

Returns Solver with its parameters changed.

• f is a function to change parameters given by its argument.

impl<L: LinAlg> Solver<L>where
    L::F: Float + Debug + LowerExp,

pub fn solve<OC, OA, OB, C>(
    self,
    (op_c, op_a, op_b, cone, work): (OC, OA, OB, C, &mut [L::F])
) -> Result<(&[L::F], &[L::F]), SolverError>where
    OC: Operator<L>,
    OA: Operator<L>,
    OB: Operator<L>,
    C: Cone<L>,

Starts to solve a conic linear program.

Returns Ok with a tuple of optimal \(x, y\) or Err with SolverError type.

• op_c is \(c\) as a linear Operator.
• op_a is \(A\) as a linear Operator.
• op_b is \(b\) as a linear Operator.
• cone is \(\mathcal{K}\) expressed by Cone.
• work slice is used for temporal variables. Solver::solve does not rely on dynamic heap allocation.