@article{57472, abstract = {{In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting.}}, author = {{Bot, Radu Ioan and Sonntag, Konstantin}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Pareto optimization, Lyapunov analysis, gradient-like dynamical systems, inertial dynamics, asymptotic vanishing damping, Tikhonov regularization, strong convergence}}, title = {{{Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}}}, year = {{2025}}, } @article{63053, author = {{Hernández, Carlos and Rodriguez-Fernandez, Angel E. and Schäpermeier, Lennart and Cuate, Oliver and Trautmann, Heike and Schütze, Oliver}}, journal = {{IEEE Transactions on Evolutionary Computation}}, keywords = {{Optimization, Evolutionary computation, Hands, Proposals, Convergence, Computational efficiency, Artificial intelligence, Accuracy, Approximation algorithms, Aerospace electronics, Multi-objective optimization, evolutionary algorithms, nearly optimal solutions, multimodal optimization, archiving, continuation}}, pages = {{1--1}}, title = {{{An Evolutionary Approach for the Computation of ∈-Locally Optimal Solutions for Multi-Objective Multimodal Optimization}}}, doi = {{10.1109/TEVC.2025.3637276}}, year = {{2025}}, } @article{32447, abstract = {{We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order \(\mathcal{O}(t^{-2})\) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.}}, author = {{Sonntag, Konstantin and Peitz, Sebastian}}, issn = {{1095-7189}}, journal = {{SIAM Journal on Optimization}}, keywords = {{multiobjective optimization, Pareto optimization, Lyapunov analysis, gradient-likedynamical systems, inertial dynamics, asymptotic vanishing damping, fast convergence}}, number = {{3}}, pages = {{2259 -- 2286}}, publisher = {{Society for Industrial and Applied Mathematics}}, title = {{{Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping}}}, doi = {{10.1137/23M1588512}}, volume = {{34}}, year = {{2024}}, } @inproceedings{17653, author = {{Polevoy, Gleb and de Weerdt, M.M.}}, booktitle = {{Proceedings of the 29th Benelux Conference on Artificial Intelligence}}, keywords = {{interaction, reciprocation, contribute, shared effort, curbing, convergence, threshold, Nash equilibrium, social welfare, efficiency, price of anarchy, price of stability}}, publisher = {{Springer}}, title = {{{Reciprocation Effort Games}}}, year = {{2017}}, } @inproceedings{48857, abstract = {{While finding minimum-cost spanning trees (MST) in undirected graphs is solvable in polynomial time, the multi-criteria minimum spanning tree problem (mcMST) is NP-hard. Interestingly, the mcMST problem has not been in focus of evolutionary computation research for a long period of time, although, its relevance for real world problems is easy to see. The available and most notable approaches by Zhou and Gen as well as by Knowles and Corne concentrate on solution encoding and on fairly dated selection mechanisms. In this work, we revisit the mcMST and focus on the mutation operators as exploratory components of evolutionary algorithms neglected so far. We investigate optimal solution characteristics to discuss current mutation strategies, identify shortcomings of these operators, and propose a sub-tree based operator which offers what we term Pareto-beneficial behavior: ensuring convergence and diversity at the same time. The operator is empirically evaluated inside modern standard evolutionary meta-heuristics for multi-criteria optimization and compared to hitherto applied mutation operators in the context of mcMST.}}, author = {{Bossek, Jakob and Grimme, Christian}}, booktitle = {{2017 IEEE Symposium Series on Computational Intelligence (SSCI)}}, keywords = {{Convergence, Encoding, Euclidean distance, Evolutionary computation, Heating systems, Optimization, Standards}}, pages = {{1–8}}, title = {{{A Pareto-Beneficial Sub-Tree Mutation for the Multi-Criteria Minimum Spanning Tree Problem}}}, doi = {{10.1109/SSCI.2017.8285183}}, year = {{2017}}, } @inproceedings{17656, author = {{Polevoy, Gleb and de Weerdt, Mathijs and Jonker, Catholijn}}, booktitle = {{Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems}}, isbn = {{978-1-4503-4239-1}}, keywords = {{agent's influence, behavior, convergence, perron-frobenius, reciprocal interaction, repeated reciprocation}}, pages = {{1431--1432}}, publisher = {{International Foundation for Autonomous Agents and Multiagent Systems}}, title = {{{The Convergence of Reciprocation}}}, year = {{2016}}, } @inproceedings{11816, abstract = {{In this paper, we consider the Maximum Likelihood (ML) estimation of the parameters of a GAUSSIAN in the presence of censored, i.e., clipped data. We show that the resulting Expectation Maximization (EM) algorithm delivers virtually biasfree and efficient estimates, and we discuss its convergence properties. We also discuss optimal classification in the presence of censored data. Censored data are frequently encountered in wireless LAN positioning systems based on the fingerprinting method employing signal strength measurements, due to the limited sensitivity of the portable devices. Experiments both on simulated and real-world data demonstrate the effectiveness of the proposed algorithms.}}, author = {{Hoang, Manh Kha and Haeb-Umbach, Reinhold}}, booktitle = {{38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013)}}, issn = {{1520-6149}}, keywords = {{Gaussian processes, Global Positioning System, convergence, expectation-maximisation algorithm, fingerprint identification, indoor radio, signal classification, wireless LAN, EM algorithm, ML estimation, WiFi indoor positioning, censored Gaussian data classification, clipped data, convergence properties, expectation maximization algorithm, fingerprinting method, maximum likelihood estimation, optimal classification, parameters estimation, portable devices sensitivity, signal strength measurements, wireless LAN positioning systems, Convergence, IEEE 802.11 Standards, Maximum likelihood estimation, Parameter estimation, Position measurement, Training, Indoor positioning, censored data, expectation maximization, signal strength, wireless LAN}}, pages = {{3721--3725}}, title = {{{Parameter estimation and classification of censored Gaussian data with application to WiFi indoor positioning}}}, doi = {{10.1109/ICASSP.2013.6638353}}, year = {{2013}}, }