Superrelaxation and the rate of convergence in minimizing quadratic functions subject to bound constraints

The paper resolves the problem concerning the rate of convergence of the working set based MPRGP (modified proportioning with reduced gradient projection) algorithm with a long steplength of the reduced projected gradient step. The main results of this paper are the formula for the R-linear rate of...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Computational optimization and applications Ročník 48; číslo 1; s. 23 - 44
Hlavní autori: Dostal, Zdenk, Domoradova, Marta, Sadowska, Marie
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.01.2011
Springer Nature B.V
Predmet:
Algorithms
Convergence
Convex and Discrete Geometry
Experiments
Inequalities
Management Science
Mathematical analysis
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Optimization
Projection
Quadratic programming
Spectra
Statistics
Studies
Bound constraints
Inexact active set strategy
Quadratic programming
Rate of convergence
Finite termination
ISSN:0926-6003, 1573-2894
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:The paper resolves the problem concerning the rate of convergence of the working set based MPRGP (modified proportioning with reduced gradient projection) algorithm with a long steplength of the reduced projected gradient step. The main results of this paper are the formula for the R-linear rate of convergence of MPRGP in terms of the spectral condition number of the Hessian matrix and the proof of the finite termination property for the problems whose solution does not satisfy the strict complementarity condition. The bound on the R-linear rate of convergence of the projected gradient is also included. For shorter steplengths these results were proved earlier by Dostál and Schöberl. The efficiency of the longer steplength is illustrated by numerical experiments. The result is an important ingredient in developming scalable algorithms for numerical solution of elliptic variational inequalities and substantiates the choice of parameters that turned out to be effective in numerical experiments.
Bibliografia:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
content type line 23
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-009-9237-6