B2 Book chapter
Proximal Bundle Method for Nonsmooth and Nonconvex Multiobjective Optimization




List of Authors: Makela MM, Karmitsa N, Wilppu O
Publisher: SPRINGER-VERLAG NEW YORK, MS INGRID CUNNINGHAM, 175 FIFTH AVE, NEW YORK, NY 10010 USA
Publication year: 2016
Book title *: Mathematical Modeling and Optimization of Complex Structures
Journal name in source: MATHEMATICAL MODELING AND OPTIMIZATION OF COMPLEX STRUCTURES
Journal acronym: COMPUT METH APPL SCI
Title of series: Computational Methods in Applied Sciences
Number in series: 40
Volume number: 40
Number of pages: 14
ISBN: 978-3-319-23563-9
eISBN: 978-3-319-23564-6

Abstract


We present a proximal bundle method for finding weakly Pareto optimal solutions to constrained nonsmooth programming problems with multiple objectives. The method is a generalization of proximal bundle approach for single objective optimization. The multiple objective functions are treated individually without employing any scalarization. The method is globally convergent and capable of handling several nonconvex locally Lipschitz continuous objective functions subject to nonlinear (possibly nondifferentiable) constraints. Under some generalized convexity assumptions, we prove that the method finds globally weakly Pareto optimal solutions. Concluding, some numerical examples illustrate the properties and applicability of the method.



Last updated on 2019-20-07 at 05:41