Lisbon Young Mathematicians Conference

Faculty of Sciences, University of Lisbon More information here

This event is aimed at PhD students, PhD and Master’s students from the University of Lisbon. During the conference, PhD and MSc students will present short papers about their current research work.

The participation of prominent guest speakers will strongly contribute to the enrichment of knowledge, inspiring young researchers.

A Direct Multisearch Filter Method for Biobjective Optimization

Abstract: Multiobjective optimization characterizes by the presence of conflicting objectives that need to be simultaneously optimized, changing the classical concept of problem solution, which is no longer a single point. In practical applications, often these functions are nonsmooth or of black-box type, preventing the use of derivative-based optimization techniques. Special algorithmic classes are required, that are able to address the multiobjective setting, not using derivatives. Direct Multisearch (DMS) is a multiobjective derivative-free optimization class of methods, with a well-established convergence analysis and competitive computational implementations, often successfully used for benchmark of new algorithms and in practical applications.

From the theoretical point of view, DMS is developed for continuous optimization with general constraints, making use of an extreme barrier approach, only evaluating feasible points. In this work, we propose the integration of a filter approach in DMS, to address biobjective optimization problems with linear and nonlinear constraints. The linear constraints are explicitly treated by the algorithm, by adapting the positive generating sets considered at each iteration to the geometry of the nearby constraints. The violations of the nonlinear constraints are aggregated in a third objective function and are treated as an additional objective to be minimized.

We will describe the proposed algorithmic structure in detail, provide results on the theoretical properties of the method, and report numerical experiments that state the performance of the proposed approach to address nonlinear constrained problems.

Key words: Derivative-free Optimization, Multiobjective Optimization, Constrained Optimization, Direct Multisearch, Filter methods methods Joint work with Andrea Brilli, Ana Luísa Custódio and Giampaolo Liuzzi.

Acknowledgments: This research was financially supported by Fundação para a Ciência e a Tecnologia (FCT) (Portuguese Foundation for Science and Technology) through projects UIDB/00297/2020,UIDP/00297/2020, UI/BD/151246/2021 (Centro de Matemática e Aplicações - NOVA Math), and PTDC/MAT-APL/28400/2017 (NOVA Math).

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