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Non-Convex Multi-Objective Optimization pp 57–95Cite as

Worst-Case Optimal Algorithms

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 123))

Abstract

The question of the possibility to construct an optimal (in some sense) algorithm is of importance to the theory of multi-objective optimization similarly to any other theory of algorithmically solvable problems. In this chapter, we aim at finding a worst-case optimal approximation of the Pareto optimal set for multi-objective optimization problems, where the convexity of objective functions is not assumed. The class of Lipschitz functions is chosen as a model of objective functions since that model is one of the simplest and best researched models of global optimization [87]. Worst-case optimal algorithms are constructed for the cases of passive (non-adaptive) and sequential (adaptive) search in [249]. These results are the generalization to the multi-objective case of the results by Sukharev who investigated the worst-case optimal single-objective optimization algorithms in [210, 211].

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Research University Higher School of Economics, Moscow, Russia

    Panos M. Pardalos

  3. Institute of Mathematics & Informatics, Vilnius University, Vilnius, Lithuania

    Antanas Žilinskas & Julius Žilinskas

Authors
  1. Panos M. Pardalos
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  2. Antanas Žilinskas
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  3. Julius Žilinskas
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Pardalos, P.M., Žilinskas, A., Žilinskas, J. (2017). Worst-Case Optimal Algorithms. In: Non-Convex Multi-Objective Optimization. Springer Optimization and Its Applications, vol 123. Springer, Cham. https://doi.org/10.1007/978-3-319-61007-8_6

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