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since 2007/10/24

Non-linear systems 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})
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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OpenOpt NLSP example >>>

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NLSP solvers

solver	license	constraints	derivatives	info
scipy_fsolve	BSD	None	df	"fsolve" is a wrapper around MINPACK's hybrd and hybrj algorithms.
nssolve	BSD	lb, ub, Aeq, A, c, h (example)	df, dc, dh	Thi one is primarily for nonsmooth and noisy funcs, uses NSP ralg solver and is intended to be enhanced from time to time, as well as ralg. ns- can be interpreted as NonSmooth or NoiSy or Naum Shor (Ukrainian academician, my teacher, r-algorithm inventor).

• if no gradient is supplied, using separate func for each nssolve equation is recommended (f = [fun1, fun2, ...]), same to c, h

The ones below work very unstable and can't use user-provided gradient, at least for scipy 0.6.0
Maybe they will be inhanced in future by someone. See here for details

• scipy_anderson
• scipy_anderson2
• scipy_broyden1
• scipy_broyden2
• scipy_broyden3
• scipy_broyden_generalized