NLLSP

Non-Linear Least Squares Problems (NLLSP)

$\mathbf {\sum_{k=0}^{K} f_k(x)^2 \to min}$

subjected to

$\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$

$\mathbf{A x} \le \mathbf{b}$

$\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}$

$\mathbf{\forall i=0,...,I: c_i(x) \le 0}$

$\mathbf{\forall j=0,...,J: h_j(x) = 0}$

$\mathbf{ \{ {f_k, c_i, h_j :R^n \to R \} \subset C^1}}$

(smooth differentiable functions)

$\mathbf{x \in R^n}$

NLLSP solvers connected to OpenOpt:

Solver	License	Made by	Info
scipy_leastsq	BSD	Argonne national laboratory, Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. more	Unconstrained problems only! "leastsq" is a scipy wrapper around MINPACK's lmdif algorithm
converter to nlp		Dmitrey	Example: r = p.solve('nlp:ralg'). See NLP page for list of available NLP solvers