Mathematical Programming

, Volume 116, Issue 1–2, pp 297–320

# A bundle-filter method for nonsmooth convex constrained optimization

FULL LENGTH PAPER

## Abstract

For solving nonsmooth convex constrained optimization problems, we propose an algorithm which combines the ideas of the proximal bundle methods with the filter strategy for evaluating candidate points. The resulting algorithm inherits some attractive features from both approaches. On the one hand, it allows effective control of the size of quadratic programming subproblems via the compression and aggregation techniques of proximal bundle methods. On the other hand, the filter criterion for accepting a candidate point as the new iterate is sometimes easier to satisfy than the usual descent condition in bundle methods. Some encouraging preliminary computational results are also reported.

## Keywords

Constrained optimization Nonsmooth convex optimization Bundle methods Filter methods

## Mathematics Subject Classification (2000)

90C30 65K05 49D27

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## Authors and Affiliations

• Elizabeth Karas
• 1
• 1
• Claudia Sagastizábal
• 2
• Mikhail Solodov
• 2
Email author
1. 1.Departamento de MatemáticaUniversidade Federal do ParanáCuritibaBrazil
2. 2.Instituto de Matemática Pura e AplicadaRio de JaneiroBrazil

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