Manual

Building problems with JuMP.jl

Currently the easiest ways to pass problems to ProxSDP is through JuMP or MathOptInterface.

In the test folder one can find MOI implementations of some problems: MIMO, Sensor Localization, Random SDPs and sdplib problems.

Solver arguments

Argument	Description	Type	Values (default)
log_verbose	print evolution of the process	`Bool`	`false`
log_freq	print evoluition of the process every n iterations	`Int`	`100`
timer_verbose	Outputs a time logger	`Bool`	`false`
time_limit	Maximum time the algorithm can try to solve in seconds	`Float64`	`360000.0`
max_iter	Maximum number of iterations	`Int`	`1000000`
tol_primal	Primal error tolerance	`Float64`	`1e-3`
tol_dual	Dual error tolerance	`Float64`	`1e-3`
tol_psd	Tolerance associated with PSD cone	`Float64`	`1e-15`
tol_soc	Tolerance associated with SOC cone	`Float64`	`1e-15`
initial_theta	Initial over relaxation parameter	`Float64`	`1.0`
initial_beta	Initial primal/dual step ratio	`Float64`	`1.0`
min_beta	Minimum primal/dual step ratio	`Float64`	`1e-4`
max_beta	Maximum primal/dual step ratio	`Float64`	`1e+4`
convergence_window	Minimum number of iterations to update target rank	`Int`	`200`
max_linsearch_steps	Maximum number of iterations for linesearch	`Int`	`1000`
full_eig_decomp	Flag for using full eigenvalue decomposition	`Bool`	`false`

JuMP example

A quick JuMP example:

using ProxSDP, JuMP

# Create a JuMP model using ProxSDP as the solver
model = Model(with_optimizer(ProxSDP.Optimizer, log_verbose=true))

# Create a Positive Semidefinite variable
@variable(model, X[1:2,1:2], PSD)

x = X[1,1]
y = X[2,2]

@constraint(model, ub_x, x <= 2)
@constraint(model, ub_y, y <= 30)
@constraint(model, con, 1x + 5y <= 3)

# ProxSDP supports maximization or minimization
# of linear functions
@objective(model, Max, 5x + 3 * y)

# Then we can solve the model
JuMP.optimize!(model)

# And ask for results!
JuMP.objective_value(model)

JuMP.value(x)
JuMP.value(y)

Referencing

The first version of the paper can be found here.

@article{souto2018exploiting,
  title={Exploiting Low-Rank Structure in Semidefinite Programming by Approximate Operator Splitting},
  author={Souto, Mario and Garcia, Joaquim D and Veiga, {\'A}lvaro},
  journal={arXiv preprint arXiv:1810.05231},
  year={2018}
}

Disclaimer

ProxSDP is a research software, therefore it should not be used in production.
Please open an issue if you find any problems, developers will try to fix and find alternatives.
ProxSDP assumes primal and dual feasibility. Currently, it is not able to reliably identify infeasibility and unboundedness.