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  5. A Direct Active Set Algorithm for Large Sparse Quadratic Programs withSimple Bounds

A Direct Active Set Algorithm for Large Sparse Quadratic Programs withSimple Bounds

File(s)
88-926.pdf (3.29 MB)
88-926.ps (767.15 KB)
Permanent Link(s)
https://hdl.handle.net/1813/6766
Collections
Computer Science Technical Reports
Author
Coleman, Thomas F.
Hulbert, Laurie
Abstract

We show how a direct active set method for solving definite and indefinite quadratic programs with simple bounds can be efficiently implemented for large sparse problems. All of the necessary factorizations can be carried out in a static data structure that is set up before the numeric computation begins. The space required for these factorizations is no larger than that required for a single sparse Cholesky factorization of a matrix with the same sparsity structure as the Hessian of the quadratic. We propose several improvements to this basic algorithm: a new way to find a search direction in the indefinite case that allows us to free more than one variable at a time and a new heuristic method for finding a starting point. These ideas are motivated by the two-norm trust region problem. Additionally, we also show how projection techniques can be used to add several constraints to the active set at each iteration. Our experimental results show that an algorithm with these improvements runs much faster than the basic algorithm for positive definite problems and finds local minima with lower function values for indefinite problems.

Date Issued
1988-07
Publisher
Cornell University
Keywords
computer science
•
technical report
Previously Published as
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR88-926
Type
technical report

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