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since 2007/10/24
OpenOpt classes and solvers
Matrix problems group
Linear Problem (LP)
f' * x -> min
subjected to
lb <= x <= ub
A*x <= b
Aeq*x = beq
Mixed-Integer Linear Problem (MILP)
f' * x -> min
subjected to
lb <= x <= ub
A*x <= b
Aeq*x = beq
xi are required to be integers for all i from intVars
xj are required to be from {0, 1} for all j from binVars
(NB! Python indexing starts from zero)
Quadratic Problem (QP)
0.5*<x,H*x> + f' * x -> min
subjected to
lb <= x <= ub
A*x <= b
Aeq*x = beq
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)
- 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)
Linear Least Absolute Values Problem (LLAVP)
||C*x-d||1 + damp*||x-X||1 -> min
subjected to
- Box - bound constraints
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- 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)
Non-linear problems group
Non-Linear Problem (NLP)
f(x) -> min
subjected to
- Box - bound constraints
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- General linear constraints
- A*x <= b
- Aeq*x = beq
- A*x <= b
- Non-linear constraints
- ci(x) <= 0, i = 0...I
- hj(x) = 0, j = 0...J
- ci(x) <= 0, i = 0...I
Non-Smooth Problem (NSP)
f(x) -> min
subjected to
- Box - bound constraints
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- General linear constraints
- A*x <= b
- Aeq*x = beq
- A*x <= b
- Non-linear constraints
- ci(x) <= 0, i = 0...I
- hj(x) = 0, j = 0...J
- ci(x) <= 0, i = 0...I
- here f(x), c(x), h(x) can be non-smooth and/or noisy
(Non-smooth problems are similar to NLP)
Non-Linear System Problem (NLSP)
Solve set of non-linear equations
F(x) = 0,
x from Rn,
F: Rn -> Rn
(or F = {Fi: Rn -> R, i = 0...n-1})
subjected to
- Box - bound constraints
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- General linear constraints
- A*x <= b
- Aeq*x = beq
- A*x <= b
- Non-linear constraints
- ci(x) <= 0, i = 0...I
- hj(x) = 0, j = 0...J
- ci(x) <= 0, i = 0...I
Least Squares Problem (LSP)
F0(x)2+F1(x)2+...+Fm(x)2 -> min,
x from Rn
subjected to
- Box - bound constraints
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- General linear constraints
- A*x <= b
- Aeq*x = beq
- A*x <= b
- Non-linear constraints
- ci(x) <= 0, i = 0...I
- hj(x) = 0, j = 0...J
- ci(x) <= 0, i = 0...I
Mini-Max Problem (MMP)
maxi { fi(x) } -> min, i=0...I subjected to
- Box - bound constraints
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- lb <= x <= ub (some coords of lb and ub can be +/- inf)
- General linear constraints
- A*x <= b
- Aeq*x = beq
- A*x <= b
- Non-linear constraints
- ci(x) <= 0, i = 0...I
- hj(x) = 0, j = 0...J
- ci(x) <= 0, i = 0...I
Global Problem (GLP)
search for global minimum of a func:
f(x) -> min
subjected to
- Box - bound constraints
- lb <= x <= ub
- lb <= x <= ub
- Linear inequality constraints
- A*x <= b
- A*x <= b
(some more constraints will be added if appropriate solver(s) will be connected)
