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Worst-Case Optimal Algorithms

In: Non-Convex Multi-Objective Optimization

Author

Listed:
  • Panos M. Pardalos

    (University of Florida
    Research University Higher School of Economics)

  • Antanas Žilinskas

    (Vilnius University)

  • Julius Žilinskas

    (Vilnius University)

Abstract

worst-case optimal 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].

Suggested Citation

  • Panos M. Pardalos & Antanas Žilinskas & Julius Žilinskas, 2017. "Worst-Case Optimal Algorithms," Springer Optimization and Its Applications, in: Non-Convex Multi-Objective Optimization, chapter 0, pages 57-95, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-61007-8_6
    DOI: 10.1007/978-3-319-61007-8_6
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