A3 Refereed book chapter or chapter in a compilation book
Multibundle Method for Constrained Nonsmooth Multiobjective DC Optimization
Authors: Joki, Kaisa; Montonen, Outi
Editors: Tuovinen, Tero; Neittaanmäki, Pekka; Knoerzer, Dietrich
Publisher: Springer Nature Switzerland
Publication year: 2026
Journal: Computational Methods in Applied Sciences
Book title : Challenges in Design Methods, Numerical Tools and Technologies for Sustainable Aviation, Transport and Industry : Commemorative publication dedicated to the 80th Jubilee of Prof. Jacques Periaux
Series title: Computational Methods in Applied Sciences
Number in series: 17
Volume: 17
First page : 39
Last page: 73
ISBN: 978-3-031-98674-1
eISBN: 978-3-031-98675-8
ISSN: 1871-3033
eISSN: 2543-0203
DOI: https://doi.org/10.1007/978-3-031-98675-8_6
Publication's open availability at the time of reporting: No Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1007/978-3-031-98675-8_6
In this paper, we MultibundleOptimizationpropose a multibundleMultibundle method. The new method is of the descent type and it is designedDesign for constrained nonsmooth multiobjective optimizationOptimization problemsProblem whose objectives and constraints can be represented as a difference of convex (DC) functionsFunction. The method combines pieces from the multiple subgradientGradient descent bundle method [49], the double bundle method [26], and the multiobjective double bundle method [47]. The idea is to find descent directions for every individual objective by using a single-objective bundle method designedDesign for DC functionsFunction, and then, form a common descent direction. The novelty in our approach is that the decision maker has an option to steer the solutionSolution process by indicating whether an individual descent direction should be used to improve one objective or should the method test the optimality. Furthermore, we present two alternative constraint handling strategies. The multibundle method is proven to have a finite convergenceConvergence to an approximate weakly Pareto stationary solutionSolution under mild assumptions. Finally, the new method is compared with a multiobjective DC method as well as a multiobjective nonconvex method to demonstrate the numericalNumerical capability of the proposed method. In addition, the constraint handling strategies are compared and some interactive examples are given.
Funding information in the publication:
The research is financially supported by Academy of Finland Projects No. 319274 led by Prof. Napsu Karmitsa and No. 310507 led by Prof. Tero Aittokallio and University of Turku.
