Title: MNH: A Derivative-Free Optimization Algorithm Using Minimal Norm Hessians
Authors: Stefan Wild
Abstract: We introduce MNH, a new algorithm for unconstrained optimization when derivatives are unavailable, primarily targeting applications that require running computationally expensive deterministic simulations. MNH relies on a trust-region framework with an underdetermined quadratic model that interpolates the function at a set of data points. We show how to construct this interpolation set to yield computationally stable parameters for the model and, in doing so, obtain an algorithm which converges to first-order critical points. Preliminary results are encouraging and show that MNH makes effective use of the points evaluated in the course of the optimization.
Keywords: Derivative-Free Optimization, Trust-Region Methods, Nonlinear Optimization, Iterative Methods
Thanks: Research supported by a DOE Computational Science Graduate Fellowship under grant number DE-FG02-97ER25308.
Status: Presented at the Tenth Copper Mountain Conference on Iterative Methods, April 2008. (Student Paper Winner)
Also Cornell University, School of Operations Research and Information Engineering Tech. Report ORIE-1466, January 2008.
Link: [PDF available from the Conference]
BibTeX:
@inproceedings{SMW08MNH,
    author      = "Stefan M. Wild",
    title       = "{MNH:} A Derivative-Free Optimization Algorithm Using Minimal Norm Hessians",
    institution = "Cornell University, School of Operations Research and Information Engineering",
    booktitle = "Tenth Copper Mountain Conference on Iterative Methods",
    month       = "April",    
    year        = "2008",
    note        = "Available at http://grandmaster.colorado.edu/~copper/2008/SCWinners/Wild.pdf"
}
	
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