Preconditioning in Large-Scale Unconstrained Optimization Problems

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dc.contributor.advisorSousedik, Bedrich
dc.contributor.authorGalambos, Emoke
dc.contributor.departmentMathematics and Statistics
dc.contributor.programMathematics and Statistics
dc.date.accessioned2021-09-01T13:55:34Z
dc.date.available2021-09-01T13:55:34Z
dc.date.issued2019-01-01
dc.description.abstractWe 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.
dc.formatapplication:pdf
dc.genretheses
dc.identifierdoi:10.13016/m2kpcv-xvec
dc.identifier.other12114
dc.identifier.urihttp://hdl.handle.net/11603/22864
dc.languageen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics and Statistics, Applied Department Collection
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.sourceOriginal File Name: Galambos_umbc_0434M_12114.pdf
dc.titlePreconditioning in Large-Scale Unconstrained Optimization Problems
dc.typeText
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