Object structure
Title:

Aproximal-Projection Bundle Method for Lagrangian Relaxation, Including Semidefine Programming

Subtitle:

Raport Badawczy = Research Report ; RB/60/2006

Creator:

Kiwiel, Krzysztof

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Date issued/created:

2006

Description:

20 pages ; 21 cm ; Bibliography p. 20

Subject and Keywords:

Nondifferentiable optimization ; Optymalizacja niezróżnicowana ; Lagrangian relaxation ; Convex programming ; Programowanie wypukłe ; Proximal bundle methods ; Semidefinite programming ; Relaksacja lagrange'a

Abstract:

The paper presents a proximal bundle method for minimizing a convex function f over a convex set C. It requires evaluating f and its subgradients with a fixed but possibly unknown accuracy ε> 0. Each iteration involves solving an unconstrained proximal subproblem and projecting a certain point onto C. The method asymptotically finds points that are ε-optimal. In Lagrangian relaxation of convex programs, it allows for ε-accurate solutions of Lagrangian subproblems and finds ε-optimal primal solutions. For semidefinite programming problems, it extends the highly successful spectral bundle method to the case of inexact eigenvalue computations.

Relation:

Raport Badawczy = Research Report

Resource type:

Text

Detailed Resource Type:

Report

Source:

RB-2006-60

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open

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