Solvers

Convex.jl depends on third-party solvers to solve optimization problems. Therefore, you will need to install one before you can solve problems with Convex.jl.

Install a solver using the Julia package manager, replacing "SCS" by Julia package name as appropriate:

import Pkg
Pkg.add("SCS")

The JuMP documentation has a list of support solvers and a list of problem classes they support.

To use a specific solver, you can use the following syntax:

julia> using Convex, SCS
julia> x = Variable();
julia> p = minimize(x, [x >= 1]);
julia> solve!(p, SCS.Optimizer)[ Info: [Convex.jl] Compilation finished: 0.0 seconds, 53.344 KiB of memory allocated
------------------------------------------------------------------
	       SCS v3.2.3 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 1, constraints m: 1
cones: 	  l: linear vars: 1
settings: eps_abs: 1.0e-04, eps_rel: 1.0e-04, eps_infeas: 1.0e-07
	  alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1
	  max_iters: 100000, normalize: 1, rho_x: 1.00e-06
	  acceleration_lookback: 10, acceleration_interval: 10
lin-sys:  sparse-direct-amd-qdldl
	  nnz(A): 1, nnz(P): 0
------------------------------------------------------------------
 iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
     0| 1.90e+01  1.00e+00  2.00e+01 -8.00e+00  1.00e-01  3.85e-05 
    25| 9.46e-06  2.35e-08  9.49e-06  1.00e+00  1.00e-01  4.99e-05 
------------------------------------------------------------------
status:  solved
timings: total: 5.06e-05s = setup: 3.03e-05s + solve: 2.02e-05s
	 lin-sys: 2.47e-06s, cones: 1.50e-06s, accel: 1.01e-06s
------------------------------------------------------------------
objective = 1.000005
------------------------------------------------------------------
Problem statistics
  problem is DCP         : true
  number of variables    : 1 (1 scalar elements)
  number of constraints  : 1 (1 scalar elements)
  number of coefficients : 1
  number of atoms        : 1

Solution summary
  termination status : OPTIMAL
  primal status      : FEASIBLE_POINT
  dual status        : FEASIBLE_POINT
  objective value    : 1.0

Expression graph
  minimize
   └─ real variable (id: 546…529)
  subject to
   └─ ≥ constraint (affine)
      └─ + (affine; real)
         ├─ real variable (id: 546…529)
         └─ [-1;;]

A different solver can be used by replacing SCS as appropriate. For example, GLPK is a mixed-inter linear solver:

julia> using GLPK
julia> solve!(p, GLPK.Optimizer)[ Info: [Convex.jl] Compilation finished: 0.0 seconds, 104.266 KiB of memory allocated
Problem statistics
  problem is DCP         : true
  number of variables    : 1 (1 scalar elements)
  number of constraints  : 1 (1 scalar elements)
  number of coefficients : 1
  number of atoms        : 1

Solution summary
  termination status : OPTIMAL
  primal status      : FEASIBLE_POINT
  dual status        : FEASIBLE_POINT
  objective value    : 1.0

Expression graph
  minimize
   └─ real variable (id: 546…529)
  subject to
   └─ ≥ constraint (affine)
      └─ + (affine; real)
         ├─ real variable (id: 546…529)
         └─ [-1;;]

Many of the solvers also allow options to be passed using MOI.OptimizerWithAttributes. For example, to set a time limit (in milliseconds) with GLPK, use:

julia> import Convex: MOI
julia> solver = MOI.OptimizerWithAttributes(GLPK.Optimizer, "tm_lim" => 60_000.0)MathOptInterface.OptimizerWithAttributes(GLPK.Optimizer, Pair{MathOptInterface.AbstractOptimizerAttribute, Any}[MathOptInterface.RawOptimizerAttribute("tm_lim") => 60000.0])
julia> solve!(p, solver)[ Info: [Convex.jl] Compilation finished: 0.05 seconds, 1.098 MiB of memory allocated
Problem statistics
  problem is DCP         : true
  number of variables    : 1 (1 scalar elements)
  number of constraints  : 1 (1 scalar elements)
  number of coefficients : 1
  number of atoms        : 1

Solution summary
  termination status : OPTIMAL
  primal status      : FEASIBLE_POINT
  dual status        : FEASIBLE_POINT
  objective value    : 1.0

Expression graph
  minimize
   └─ real variable (id: 546…529)
  subject to
   └─ ≥ constraint (affine)
      └─ + (affine; real)
         ├─ real variable (id: 546…529)
         └─ [-1;;]

As another example, if we wish to turn off printing for the SCS solver (that is, run in quiet mode), we can do so as follows:

julia> silent_scs = MOI.OptimizerWithAttributes(SCS.Optimizer, MOI.Silent() => true)MathOptInterface.OptimizerWithAttributes(SCS.Optimizer, Pair{MathOptInterface.AbstractOptimizerAttribute, Any}[MathOptInterface.Silent() => true])
julia> solve!(p, silent_scs)[ Info: [Convex.jl] Compilation finished: 0.0 seconds, 54.453 KiB of memory allocated
Problem statistics
  problem is DCP         : true
  number of variables    : 1 (1 scalar elements)
  number of constraints  : 1 (1 scalar elements)
  number of coefficients : 1
  number of atoms        : 1

Solution summary
  termination status : OPTIMAL
  primal status      : FEASIBLE_POINT
  dual status        : FEASIBLE_POINT
  objective value    : 1.0

Expression graph
  minimize
   └─ real variable (id: 546…529)
  subject to
   └─ ≥ constraint (affine)
      └─ + (affine; real)
         ├─ real variable (id: 546…529)
         └─ [-1;;]

Another option is to use the solver-independent silent keyword argument to solve!:

julia> solve!(p, SCS.Optimizer; silent=true)Problem statistics
  problem is DCP         : true
  number of variables    : 1 (1 scalar elements)
  number of constraints  : 1 (1 scalar elements)
  number of coefficients : 1
  number of atoms        : 1

Solution summary
  termination status : OPTIMAL
  primal status      : FEASIBLE_POINT
  dual status        : FEASIBLE_POINT
  objective value    : 1.0

Expression graph
  minimize
   └─ real variable (id: 546…529)
  subject to
   └─ ≥ constraint (affine)
      └─ + (affine; real)
         ├─ real variable (id: 546…529)
         └─ [-1;;]

See each solver's documentation for more information on solver-dependent options.