1. What are the nature of your constraints? "optim" will optimize a function with optional box constraints. "constrOptim" will optimize a function subject to linear inequality constraints.
2. If you want to estimate the p[i]'s, i = 1, ..., k, I would recommend a multivariate logistic transformation to (k-1) unconstrained variables. I have had serious difficulties with constrained optimizers testing values outside the constraints and then stopping because the objective function misbehaved. I don't know if "optim" does this, but I don't even try constrained optimization if I can find a sensible, unconstrained parameterization. Often, confidence regions, etc., are better behaved in the unconstrained space as well.
hope this helps. spencer graves
Simon Wood wrote:
Hello. I have searched the archives but have not found anything. I need to solve a constrained optimisation problem for a nonlinear function (?maximum entropy formalism?). Specifically,
Optimise: -1*SUM(p_ilog(p_i)) for a vector p_i of probabilities, conditional on a series of constraints of the form:
SUM(T_i*p_i)=k_i for given values of T_i and k_i (these are constraints on expectations).
A better answer may exist to this question, but here goes anyway.... Could you use sequential quaratic programming here (i.e. just constrain the QP problem generated at each iterate of Newton's method)? There's an R library for quadratic programming....
Simon
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Simon Wood [EMAIL PROTECTED] www.stats.gla.ac.uk/~simon/
Department of Statistics, University of Glasgow, Glasgow, G12 8QQ
Direct telephone: (0)141 330 4530 Fax: (0)141 330 4814
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