Minimizing quadratic functions with semidefinite Hessian subject to bound constraints

The MPRGP (modified proportioning with reduced gradient projections) algorithm for minimization of the strictly convex quadratic function subject to bound constraints is adapted to the solution of problems with a semidefinite Hessian A. The adapted algorithm accepts the decrease directions that belo...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) Vol. 70; no. 8; pp. 2014 - 2028
Main Authors: Dostal, Zdenk, Pospisil, Lukas
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.10.2015
Subjects:
Algorithms
Bound constraints
Contact
Mathematical models
Optimization
Projection
Quadratic equations
Quadratic programming
Semidefinite Hessian
Spectra
Three dimensional
Quadratic programming
Bound constraints
Semidefinite Hessian
ISSN:0898-1221, 1873-7668
Online Access:Get full text
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Summary:The MPRGP (modified proportioning with reduced gradient projections) algorithm for minimization of the strictly convex quadratic function subject to bound constraints is adapted to the solution of problems with a semidefinite Hessian A. The adapted algorithm accepts the decrease directions that belong to the null space of A and generates the iterates that are proved to minimize the cost function. The paper examines specific features of the solution of the problems with convex, but not necessarily strictly convex Hessian. The performance of the algorithm is demonstrated by the solution of a semi-coercive contact problem of elasticity and a 3D particle dynamics problem. The results are compared with those obtained by the spectral projected gradient method and the projected-Jacobi method.
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2015.08.015