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A. L. Custódio (alcustodiofct.unl.pt) Abstract: Direct Multisearch (DMS) 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 the DMS algorithm takes at most $\mathcal{O}(L(\epsilon)\epsilon^{2m})$ iterations for driving a criticality measure below $\epsilon>0$ (here $m$ represents the number of components of the objective function and $L(\epsilon)$ the cardinality of the approximation to the Pareto front). We then focus on a particular instance of DMS, which considers a more strict criterion for accepting new nondominated points. In this case, we can establish a better worstcase complexity bound of $\mathcal{O}(\epsilon^{2})$ for driving the same criticality measure below $\epsilon>0$. 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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