# Matlab¶

## Setup¶

The solver is initialized by creating an OSQP object

m = osqp;


The problem is specified in the setup phase by running

m.setup(P, q, A, l, u, varargin)


The arguments q, l and u are arrays. The elements of l and u can be $$\pm \infty$$ ( using Inf). The arguments P and A are sparse matrices. Matrix P can be either complete or just the upper triangular part. OSQP will make use of only the upper triangular part.

There is no need to specify all the problem data. They can be omitted by writing [].

The last argument varargin specifies the solver options. You can pass the options in two ways. You can either set the individual parameters as field-value pairs, e.g.,

m.setup(P, q, A, l, u, 'eps_abs', 1e-04, 'eps_rel', 1e-04);


Alternatively, you can create a structure containing all the settings, change some of the fields and then pass it as the last argument

settings = m.default_settings();
settings.eps_abs = 1e-04;
settings.eps_rel = 1e-04;
m.setup(P, q, A, l, u, settings);


The allowed settings are defined in Solver settings.

## Solve¶

The problem can be solved by

results = m.solve();


The results structure contains the primal solution x, the dual solution y, certificate of primal infeasibility prim_inf_cert, certificate of dual infeasibility dual_inf_cert and the info structure containing the solver statistics defined in the following table

Member

Description

iter

Number of iterations

status

Solver status

status_val

Solver status value as in Status values

status_polish

Polishing status

obj_val

Objective value

pri_res

Primal residual

dua_res

Dual residual

setup_time

Setup time

solve_time

Solve time

update_time

Update time

polish_time

Polish time

run_time

Total run time: setup/update + solve + polish

rho_estimate

Optimal rho estimate

rho_updates

Note that if multiple solves are executed from single setup, then after the first one run_time includes update_time + solve_time + polish_time.

## Update¶

Part of problem data and settings can be updated without requiring a new problem setup.

### Update problem vectors¶

Vectors q, l and u can be updated with new values q_new, l_new and u_new by just running

m.update('q', q_new, 'l', l_new, 'u', u_new);


The user does not have to specify all the arguments.

### Update problem matrices¶

Matrices A and P can be updated by changing the value of their elements but not their sparsity pattern. The interface is designed to mimic the C/C++ counterpart with the Matlab 1-based indexing. Note that the new values of P represent only the upper triangular part while A is always represented as a full matrix.

You can update the values of all the elements of P by executing

m.update('Px', Px_new)


If you want to update only some elements, you can pass

m.update('Px', Px_new, 'Px_idx', Px_new_idx)


where Px_new_idx is the vector of indices of mapping the elements of Px_new to the original vector Px representing the data of the sparse matrix P.

Matrix A can be changed in the same way. You can also change both matrices at the same time by running, for example

m.update('Px', Px_new, 'Px_idx', Px_new_idx, 'Ax' Ax_new, 'Ax', Ax_new_idx)


### Update settings¶

Settings can be updated by running

m.update_settings(varargin);


where varargin argument is described in Setup. The allowed settings that can be updated are marked with an * in Solver settings.

## Warm start¶

OSQP automatically warm starts primal and dual variables from the previous QP solution. If you would like to warm start their values manually, you can use

m.warm_start('x', x0, 'y', y0)


where x0 and y0 are the new primal and dual variables.