Worst-Case Optimal Algorithms

Panos M. Pardalos, Antanas Žilinskas and Julius Žilinskas
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Panos M. Pardalos: University of Florida
Antanas Žilinskas: Vilnius University
Julius Žilinskas: Vilnius University

Chapter Chapter 6 in Non-Convex Multi-Objective Optimization, 2017, pp 57-95 from Springer

Abstract: 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].

Date: 2017
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DOI: 10.1007/978-3-319-61007-8_6

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