qics.Solver

class qics.Solver(model, max_iter=100, max_time=3600, tol_gap=1e-08, tol_feas=1e-08, tol_infeas=1e-12, tol_ip=1e-13, tol_near=1000.0, verbose=2, ir=True, toa=True, init_pnt=None, use_invhess=None)

A class representing an instance of a solver, and is parameterized by a conic program model and adjustable solver settings.

Parameters:

modelModel

Representation of a given conic program.

max_iterint, optional

Maximum number of solver iterations before terminating. The default is 100.

max_timefloat, optional

Maximum time elapsed, in seconds, before terminating. The default is 3600.

tol_gapfloat, optional

Stopping tolerance for (relative) optimality gap. The default is 1e-8.

tol_feasfloat, optional

Stopping tolerance for (relative) primal and dual feasibility. The default is 1e-8.

tol_infeasfloat, optional

Tolerance for detecting infeasible problem. The default is 1e-12.

tol_ipfloat, optional

Tolerance for detecting ill-posed problem. The default is 1e-13.

tol_nearfloat, optional

Allowable margin for certifying near optimality when solver is stopped early. The default is 1e3.

verbose{0, 1, 2, 3}, optional

Verbosity level of the solver, where

• 0 : No output.

• 1 : Only print problem and solution summary.

• 2 : Also print summary of the solver at each iteration.

• 3 : Also print summary of the stepper at each iteration.

The default is 2.

irbool, optional

Whether to use iterative refinement when solving the KKT system. The default is True.

toabool, optional

Whether to use third-order adjustments to improve the stepping directions. The default is True.

init_pntPoint, optional

Where to initialize the interior-point algorithm from. Variables which contain nan are flagged to be intialized using the default initialization method. The default is None, which intializes all variables using the default method.

use_invhessbool, optional

Whether or not to avoid using inverse Hessian product oracles by solving a modified cone program with \(G^{-1}(\mathcal{K})=\{ x : Gx \in \mathcal{K} \}\). By default, this is False if \(G\neq-\mathbb{I}\), \(G\) is full column rank, and \(\mathcal{K}\) mainly consists of QuantRelEntr, OpPerspecEpi, and OpPerspecTr cones, and is True otherwise.

solve()

Run the primal-dual interior point solver for a given problem model.

Returns:

dict

Dictionary which summarizes the solution of a conic program. Contains the following keys.

• x_opt (ndarray) : Optimal primal variable \(x^*\).

• y_opt (ndarray) : Optimal dual variable \(y^*\).

• z_opt (VecProduct) : Optimal dual variable \(z^*\).

• s_opt (VecProduct) : Optimal primal variable \(s^*=h-Gx^*\).

• sol_status (string) : Solution status. Can either be:

  • optimal : Primal-dual optimal solution reached

  • pinfeas : Detected primal infeasibility

  • dinfeas : Detected dual infeasibility

  • near_optimal : Near primal-dual optimal solution

  • near_pinfeas : Near primal infeasibility

  • near_dinfeas : Near dual infeasibiltiy

  • illposed : Problem is ill-posed

  • unknown : Unknown solution status

• exit_status (string) : Solver exit status. Can either be:

  • solved : Terminated at desired tolerance

  • max_iter : Exceeded maximum allowable iterations

  • max_time : Exceeded maximum allowable time

  • step_failure : Unable to take another step

  • slow_progress: Residuals are decreasing too slowly

• num_iter (int) : Number of solver iterations.

• solve_time (float) : Total time elapsed (in seconds).

• p_obj (float) : Optimal primal objective \(c^\top x^*\).

• d_obj (float) : Optimal dual objective \(-b^\top y^* - h^\top z^*\).

• opt_gap (float) : Relative optimality gap.

• p_feas (float) : Relative primal feasibility.

• d_feas (float) : Relative dual feasibiltiy.