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since 2007/10/24

OpenOpt classes and solvers

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Here you can classify your problem according to the list below and then choose appropriate solver.

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Linear Problem (LP)

f' * x -> min
subjected to
lb <= x <= ub
A*x <= b
Aeq*x = beq

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Mixed-Integer Linear Problem (MILP)

f' * x -> min
subjected to
lb <= x <= ub
A*x <= b
Aeq*x = beq
x_i are required to be integers for all i from intVars
x_j are required to be from {0, 1} for all j from binVars
(NB! Python indexing starts from zero)

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Quadratic Problem (QP)

0.5*<x,H*x> + f' * x -> min
subjected to
lb <= x <= ub
A*x <= b
Aeq*x = beq

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Non-Linear Problem (NLP)

f(x) -> min
subjected to

• Box - bound constraints
  • lb <= x <= ub (some coords of lb and ub can be +/- inf)
    
• General linear constraints
  • A*x <= b
    
  • Aeq*x = beq
    
• Non-linear constraints
  • c_i(x) <= 0, i = 0...I
    
  • h_j(x) = 0, j = 0...J
    

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Non-Smooth Problem (NSP)

f(x) -> min
subjected to

• Box - bound constraints
  • lb <= x <= ub (some coords of lb and ub can be +/- inf)
    
• General linear constraints
  • A*x <= b
    
  • Aeq*x = beq
    
• Non-linear constraints
  • c_i(x) <= 0, i = 0...I
    
  • h_j(x) = 0, j = 0...J
    
• here f(x), c(x), h(x) can be non-smooth and/or noisy

(Non-smooth problems are similar to NLP)

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Non-Linear Solve Problem (NLSP)

Solve set of non-linear equations
F(x) = 0,
x from Rⁿ,
F: Rⁿ -> Rⁿ
(or F = {F_i: Rⁿ -> R, i = 0...n-1})

subjected to

• Box - bound constraints
  • lb <= x <= ub (some coords of lb and ub can be +/- inf)
    
• General linear constraints
  • A*x <= b
    
  • Aeq*x = beq
    
• Non-linear constraints
  • c_i(x) <= 0, i = 0...I
    
  • h_j(x) = 0, j = 0...J
    

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Least Squares Problem (LSP)

Solve set of non-linear equations in sense of least squares
Sum_i (F_i(x))² -> min,
i = 0...m,
x from Rⁿ

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Linear Least Squares Problem (LLSP)

    0.5*||C*x-d||2 + 0.5*damp*||x-X||2 + fTx-> min

subjected to

• Box - bound constraints
  • lb <= x <= ub (some coords of lb and ub can be +/- inf)
    

(some more constraints will be added if appropriate solver(s) will be connected)

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Mini-Max Problem (MMP)

max_i { f_i(x) } -> min, i=0...I

subjected to

• Box - bound constraints
  • lb <= x <= ub (some coords of lb and ub can be +/- inf)
    
• General linear constraints
  • A*x <= b
    
  • Aeq*x = beq
    
• Non-linear constraints
  • c_i(x) <= 0, i = 0...I
    
  • h_j(x) = 0, j = 0...J
    

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Global Problem (GLP)

search for global minimum of a func:
f(x) -> min
subjected to

• Box - bound constraints
  • lb <= x <= ub
    

(some more constraints will be added if appropriate solver(s) will be connected)