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What is the most suitable optimization algorithm for optimizing maximum likelihood estimator? In excel I used GRG non linear optimization algorithm, is that good enough?

I want to write my own code to understand optimization better so I want to choose most suitable non linear constrained optimization algo for MLE.

Cheers

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GRG is a good and robust constrained optimization algorithm. However GRG gives only local solution it may be worthwhile to use an evolutionary solver and obtain the initial estimates and then use the solution obtained using evolutional algorithm as a starting point for GRG to obtain robust optimal solution. You can do this using excel solver.

R has it own library for mle estimation. It also has a function called optim for unconstrained optimization and does not have GRG. You can further check out the optimization cran task view [website][1] for R which has both constrained and unconstrained optimization routines in R

If you post the problem, may be I could provide some additional insights.

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  • $\begingroup$ Hi, thanks for reply. I'm trying to code Optimizer myself to understand it well. I wrote BFGS optimization algorithm in Java and use Wolfe Conditions for Line search and it is producing global minimum. Used Rosenbrock function as my test fixture. But BFGS I wrote is unconstrained optimizer. If I want to use BFGS algo for GARCH MLE then I need to modify it to constrained optimization algorithm to satisfy MLE constraints. But before going ahead I want to know whether constrained BFGS algo is better suited to solve GARCH MLE like problems. Thanks for your time. $\endgroup$ Dec 18 '13 at 5:22
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I had good experience with stochastic search methods. They basically create a set of markov-chains and sample the parameter space around previous estimates. They work well in situations with objective functions who have multiple local maxima/minima, strong discontinuities or costly function evaluations. Some of the algorithms even work well for stochastic functions.

Easy to implement algorithms include ASA (adaptive simulated annealing), DDS (dynamical dimensioned search), DE (differential evolution) or the adaptive variant JADE (which I use).

More complex algorithms include CMA(-ES) (Covariance matrix adaption) or surrogate assisted techniques like kriging.

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  • $\begingroup$ I am trying to perform maximization on historical data to calibrate GARCH parameters. So I guess there are enough deterministic methods to achieve the same? Do I need stochastic methods? Cheers $\endgroup$ Dec 19 '13 at 7:46

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