Preconditioning in Large-Scale Unconstrained Optimization Problems
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Date
2019-01-01
Type of Work
Department
Mathematics and Statistics
Program
Mathematics and Statistics
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Access limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan thorugh a local library, pending author/copyright holder's permission.
This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu
This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu
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Abstract
We investigate the effects of preconditioning on the convergence of the L-BFGS method. Our goal is to find a global minimum of a non-convex, differentiable function, using non-preconditioned and linearly preconditioned L-BFGS algorithms. The objective function is a 6-dimensional variation of the Bohachevsky N.1 benchmark function, with a dominant convex part. We discuss some numerical instability issues caused by ill-conditioned systems and the non-convexity of the objective function. We also introduce a new algorithm, which combines the preconditioned and non-preconditioned L-BFGS algorithms with the Cat Swarm Optimization Algorithm. The implemented algorithm solves the numerical instability issues and complements the optimization problem with a randomized global search. The results will show the improved performance of the algorithm when used with preconditioning.