Multiple subgradient descent bundle method for convex nonsmooth multiobjective optimization




Outi Montonen, Napsu Karmitsa, Marko M. Mäkelä

PublisherTaylor & Francis

2018

Optimization

67

1

139

158

20

0233-1934

1029-4945

DOIhttps://doi.org/10.1080/02331934.2017.1387259

https://research.utu.fi/converis/portal/Publication/27435042



The aim of this paper is to propose a new multiple subgradient descent bundle method for solving unconstrained convex nonsmooth multiobjective optimization problems. Contrary to many existing multiobjective optimization methods, our method treats the objective functions as they are without employing a scalarization in a classical sense. The main idea of this method is to find descent directions for every objective function separately by utilizing the proximal bundle approach, and then trying to form a common descent direction for every objective function. In addition, we prove that the method is convergent and it finds weakly Pareto



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