Julia¶
Setup¶
The solver is initialized by creating an OSQP Model
m = OSQP.Model()
The problem is specified in the setup phase by running
OSQP.setup!(m; P=P, q=q, A=A, l=l, u=u, settings...)
The arguments q
, l
and u
are Vector{Float64}
.
The elements of l
and u
can be \(\pm \infty\) ( using Inf
).
The arguments P
and A
are sparse matrices of type SparseMatrixCSC
.
Matrix P
can be either complete or just the upper triangular
part. OSQP will make use of only the upper triangular part.
If they are sparse matrices are in another format, the interface will attempt to convert them.
There is no need to specify all the arguments.
The argument settings
specifies the solver settings.
Settings can also be passed as indipendent keyword arguments such as max_iter=1000
.
The allowed parameters are defined in Solver settings.
Solve¶
The problem can be solved by
results = OSQP.solve!(m)
The output results
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
object containing the solver statistics defined in the following table
Member 
Description 


Number of iterations 

Solver status 

Solver status value as in Status values 

Polishing status 

Objective value 

Primal residual 

Dual residual 

Setup time 

Solve time 

Update time 

Polish time 

Total run time: setup/update + solve + polish 

Optimal rho estimate 

Number of 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
OSQP.update!(m; q=q_new, l=l_new, u=u_new)
The user does not have to specify all the keyword 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 Julia 1based 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
OSQP.update!(m, Px=Px_new)
If you want to update only some elements, you can pass
OSQP.update!(m, 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
OSQP.update!(m, Px=Px_new, Px_idx=Px_new_idx, Ax=Ax_new, Ax=Ax_new_idx)
Update settings¶
Settings can be updated by running
OSQP.update_settings!(m; new_settings)
where new_settings
are the new settings specified as keyword arguments that can be updated which 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
OSQP.warm_start!(m; x=x0, y=y0)
where x0
and y0
are the new primal and dual variables.