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using MathProgBase



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# examples from http://mathprogbasejl.readthedocs.io/en/latest/linprog.html



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methods(linprog)









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4 methods for generic function linprog: linprog(c::Union{Array{T<:Union{Char,Real},1},Char,Real}, A::AbstractArray{T<:Any,2}, rowlb::Union{Array{T<:Union{Char,Real},1},Char,Real}, rowub::Union{Array{T<:Union{Char,Real},1},Char,Real}, lb::Union{Array{T<:Union{Char,Real},1},Char,Real}, ub::Union{Array{T<:Union{Char,Real},1},Char,Real}) at /opt/julia_packages/.julia/v0.5/MathProgBase/src/HighLevelInterface/linprog.jl:95
  linprog(c::Union{Array{T<:Union{Char,Real},1},Char,Real}, A::AbstractArray{T<:Any,2}, rowlb::Union{Array{T<:Union{Char,Real},1},Char,Real}, rowub::Union{Array{T<:Union{Char,Real},1},Char,Real}, lb::Union{Array{T<:Union{Char,Real},1},Char,Real}, ub::Union{Array{T<:Union{Char,Real},1},Char,Real}, solver::MathProgBase.SolverInterface.AbstractMathProgSolver) at /opt/julia_packages/.julia/v0.5/MathProgBase/src/HighLevelInterface/linprog.jl:95
  linprog(c, A, rowlb, rowub) at /opt/julia_packages/.julia/v0.5/MathProgBase/src/HighLevelInterface/linprog.jl:99
  linprog(c, A, rowlb, rowub, solver::MathProgBase.SolverInterface.AbstractMathProgSolver) at /opt/julia_packages/.julia/v0.5/MathProgBase/src/HighLevelInterface/linprog.jl:99

\begin{split}\min_{x,y}\quad &-x\\ s.t. \quad &2x + y \leq 1.5\\ & x \geq 0, y \geq 0\end{split}

Form 1

linprog(c, A, lb, ub, l, u)

\begin{split}\min_{x}\quad &c^Tx\\ s.t.\quad &lb \leq Ax \leq ub\\ &l \leq x \leq u\\\end{split}



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sol = linprog([-1,0],[2 1],-Inf,1.5,0,Inf)









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MathProgBase.HighLevelInterface.LinprogSolution(:Optimal,-0.75,[0.75,0.0],Dict{Any,Any}(Pair{Any,Any}(:redcost,[0.0,0.5]),Pair{Any,Any}(:lambda,[-0.5])))

Form 1'

(shortcut with implicit [0,Inf] constraints)



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sol = linprog([-1,0],[2 1],-Inf,1.5)









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MathProgBase.HighLevelInterface.LinprogSolution(:Optimal,-0.75,[0.75,0.0],Dict{Any,Any}(Pair{Any,Any}(:redcost,[0.0,0.5]),Pair{Any,Any}(:lambda,[-0.5])))

Form 2

linprog(c, A, sense, b, l, u)

\begin{split}\min_{x}\quad &c^Tx\\ s.t. \quad &a_i^Tx \text{ sense}_i \, b_i \forall\,\, i\\ &l \leq x \leq u\\\end{split}



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sol = linprog([-1,0],[2 1],'<',1.5)









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MathProgBase.HighLevelInterface.LinprogSolution(:Optimal,-0.75,[0.75,0.0],Dict{Any,Any}(Pair{Any,Any}(:redcost,[0.0,0.5]),Pair{Any,Any}(:lambda,[-0.5])))



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sol = linprog([-1,0],[2 1; 1 0],['<','>'],[1.5; 0.25])









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MathProgBase.HighLevelInterface.LinprogSolution(:Optimal,-0.75,[0.75,0.0],Dict{Any,Any}(Pair{Any,Any}(:redcost,[0.0,0.5]),Pair{Any,Any}(:lambda,[-0.5,0.0])))