Using warm start feature of PATHSolver

[hhoeschle]

@AndradeTiago has developed the possibility of using a warm start for the PATHSolver and provided the code in a pull request: https://github.com/chkwon/PATHSolver.jl/pull/25

Using the feature requires some changes to the Complementarity Package. I have setup a test and will put the changes here:

• adding the start value to the type:

  type ComplementarityType
  lb::Float64
  var::JuMP.Variable
  ub::Float64
  start::Float64
  F::JuMP.NonlinearExpression
  lin_idx::Int
  var_name::String
  F_name::String
  end

• initialize starting value

  function add_complementarity(m::JuMP.Model, var::JuMP.Variable, F::JuMP.NonlinearExpression, F_name::String)
  lb = getlowerbound(var)
  ub = getupperbound(var)
  var_name = getname(var)
  if !isnan(getvalue(var))
    start = getvalue(var)
  else
    start = lb
  end
  new_dimension = ComplementarityType(lb, var, ub, start, F, linearindex(var), var_name, F_name)
  mcp_data = getMCPData(m)
  push!(mcp_data, new_dimension)
  end

• initialize the starting value in linear index (for now i have put in the function getBoundsLinearIndex)

  function getBoundsLinearIndex(mcp_data)
  n = length(mcp_data)
  lb = zeros(n)
  ub = ones(n)
  start = zeros(n)
  for i in 1:n
      @show mcp_data[i]
      lb[linearindex(mcp_data[i].var)] = mcp_data[i].lb
      ub[linearindex(mcp_data[i].var)] = mcp_data[i].ub
      start[linearindex(mcp_data[i].var)] = mcp_data[i].start
  end
  return lb, ub, start
  end

• retrieve the value in _solve_path(m::Model; linear=false)

  lb, ub, start = getBoundsLinearIndex(mcp_data)

• include the start value when calling the PATHSolver.solveMCP/LCP

  if linear==true
      J0 = myjac(zeros(size(lb)))
      Jr = myjac(100*rand(size(ub)))
  
      if norm(J0-Jr, 1) > 10e-8
          error("The mappings do not seem linear. Rerun 'solveMCP()' after removing 'linear=true'.")
      end
  
      status, z, f = PATHSolver.solveLCP(myfunc, J0, lb, ub, var_name, F_name, start)
  
  else
      status, z, f = PATHSolver.solveMCP(myfunc, myjac, lb, ub, var_name, F_name, start)
  end

[hhoeschle]

The transport test in example/mcp/transmcp.jl could be extended as follows:

    w_start = Dict("seattle"=> 0, "san-diego"=>0)
    @variable(m, w[i in plants] >= 0, start=w_start[i])

    p_start = Dict("new-york"=>0.225, "chicago"=>0.153, "topeka"=>0.126)
    @variable(m, p[j in markets] >= 0, start=p_start[j])

    x_start = Dict(
        ("seattle","new-york")=>50,
        ("seattle","chicago")=>300,
        ("seattle","topeka")=>0,
        ("san-diego","new-york")=>275,
        ("san-diego","chicago")=>0,
        ("san-diego","topeka")=>275,
        )
    @variable(m, x[i in plants, j in markets] >= 0, start=x_start[(i,j)])

[chkwon]

warmstart is enabled now.

[hhoeschle]

Very well done. I have had some first tests today and I am super happy with the time saving because of new feature.

[chkwon]

Glad that it worked out nicely for you. Sorry for taking long time.