- Worst-case complexity bounds of directional direct-search methods for multiobjective derivative-free optimization A. L. Custódio (alcustodiofct.unl.pt) Y. Diouane (youssef.diouaneisae.fr) R. Garmanjani (r.garmanjanifct.unl.pt) E. Riccietti (elisa.ricciettienseeiht.fr) Abstract: Direct Multisearch (DMS) is a well-established class of algorithms, suited for multiobjective derivative-free optimization. In this work, we analyze the worst-case 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 worst-case complexity bound of $\mathcal{O}(\epsilon^{-2})$ for driving the same criticality measure below $\epsilon>0$. Keywords: Multiobjective unconstrained optimization; Derivative-free optimization methods; Directional direct-search; Worst-case complexity; Nonconvex smooth optimization Category 1: Nonlinear Optimization Category 2: Nonlinear Optimization (Unconstrained Optimization ) Citation: Download: [PDF]Entry Submitted: 09/19/2019Entry Accepted: 09/19/2019Entry Last Modified: 08/04/2020Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.