Package 'ROI.plugin.osqp'

osqp

Description

This package provides an interface to OSQP. The OSQP solver is a numerical optimization package or solving convex quadratic programs written in C and based on the alternating direction method of multipliers.

Control Arguments

The following description of the control parameters is mostly copied from the osqp manual.

• [] rho ADMM step rho

• [] sigma ADMM step sigma

• [] max_iter maximum iterations

• [] abs_tol absolute convergence tolerance

• [] rel_tol relative convergence tolerance

• [] eps_prim_inf primal infeasibility tolerance

• [] eps_dual_inf dual infeasibility tolerance

• [] alpha relaxation parameter

• [] linsys_solver which linear systems solver to use, 0=QDLDL, 1=MKL Pardiso

• [] delta regularization parameter for polish

• [] polish boolean, polish ADMM solution

• [] polish_refine_iter iterative refinement steps in polish

• [] verbose boolean, write out progress

• [] scaled_termination boolean, use scaled termination criteria

• [] check_termination integer, check termination interval. If 0, termination checking is disabled

• [] warm_start boolean, warm start

• [] scaling heuristic data scaling iterations. If 0, scaling disabled

• [] adaptive_rho cboolean, is rho step size adaptive?

• [] adaptive_rho_interval Number of iterations between rho adaptations rho. If 0, it is automatic

• [] adaptive_rho_tolerance Tolerance X for adapting rho. The new rho has to be X times larger or 1/X times smaller than the current one to trigger a new factorization

• [] adaptive_rho_fraction Interval for adapting rho (fraction of the setup time)

References

Bartolomeo Stellato and Goran Banjac and Paul Goulart and Alberto Bemporad and Stephen Boyd. OSQP: An Operator Splitting Solver for Quadratic Programs https://arxiv.org/abs/1711.08013, 2017

Bartolomeo Stellato and Goran Banjac. OSQP “webpage” https://osqp.org/, 2019

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Quadratic Problem 1

Description

$maximize \ \ x_1^2 + x_2^2 + x_3^2 - 5 x_2$

$subject \ to:$

$-4 x_1 - 3 x_2 + \geq -8$

$2 x_1 + x_2 + \geq 2$

$- 2 x_2 + x_3 \geq 0$

$x_1, x_2, x_3 \geq 0$

Examples

require("ROI")
require("ROI.plugin.osqp")

A <- cbind(c(-4, -3, 0), 
           c( 2,  1, 0), 
           c( 0, -2, 1))
x <- OP(Q_objective(diag(3), L =  c(0, -5, 0)),
        L_constraint(L = t(A),
                     dir = rep(">=", 3),
                     rhs = c(-8, 2, 0)))

opt <- ROI_solve(x, solver = "osqp", abs_tol = 1e-8, rel_tol = 1e-8)
opt
## Optimal solution found.
## The objective value is: -2.380952e+00
solution(opt)
## [1] 0.4761905 1.0476191 2.0952381

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