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A. L. Custódio (alcustodiofct.unl.pt) Abstract: Direct Multisearch is a wellestablished class of algorithms, suited for multiobjective derivativefree optimization. In this work, we analyze the worstcase complexity of this class of methods in its most general formulation for unconstrained optimization. Considering nonconvex smooth functions, we show that to drive a given criticality measure below a specific positive threshold, Direct Multisearch takes at most a number of iterations proportional to the square of the inverse of the threshold, raised to the number of components of the objective function. This number is also proportional to the size of the set of linked sequences between the first unsuccessful iteration and the iteration immediately before the one where the criticality condition is satisfied. We then focus on a particular instance of Direct Multisearch, which considers a more strict criterion for accepting new nondominated points. In this case, we can establish a better worstcase complexity bound, simply proportional to the square of the inverse of the threshold, for driving the same criticality measure below the considered threshold. Keywords: Multiobjective unconstrained optimization; Derivativefree optimization methods; Directional directsearch; Worstcase complexity; Nonconvex smooth optimization Category 1: Nonlinear Optimization Category 2: Nonlinear Optimization (Unconstrained Optimization ) Citation: Download: [PDF] Entry Submitted: 09/19/2019 Modify/Update this entry  
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