INFORMATICA International Journal Main Page Editorial Board Abstracting/Indexing Instructions to Authors Subscription Information Contents Author Index Papers in Production		INFORMATICA, 2011, Vol. 22, No. 4, 521-536 © Institute of Mathematics and Informatics, ISSN 0868-4952 On the Pareto Optimality in the Context of Lipschitzian Optimization Jonas MOCKUS Vilnius University, Institute of Mathematics and Informatics Akademijos 4, LT-08663 Vilnius, Lithuania E-mail: jmockus@gmail.com Abstract A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown. To address that, we propose a novel method called Pareto-Lipschitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitz constants. In the proposed approach, a set of all unknown Lipschitz constants is regarded as multiple criteria using the concept of Pareto Optimality (PO). We compare PLO to the existing algorithm DIRECT. We show that, in contrast to PLO, the DIRECT algorithm considers only a small subset of PO decisions that are selected by a heuristic rule depending on an adjustable parameter.It means that some PO decisions are preferred to others. By contrast, PLO regards all PO decisions without preferences and is naturally suited to utilize highly parallel computing. Keywords: Pareto optimality, Lipschitz functions, global optimization To preview Lithuanian abstract see full article text To preview full article text in PDF format click here You could obtain free Acrobat Reader from Adobe
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