Minimizing quadratic functions with separable quadratic constraints

Authors:
R. Kucera
Affiliations:
VSB-Technical University, Ostrava, Czech Republic
Venue:
Optimization Methods & Software
Year:
2007

Citing 5
Cited 2

Practical methods of optimization; (2nd ed.)

Practical methods of optimization; (2nd ed.)
Box Constrained Quadratic Programming with Proportioning and Projections

SIAM Journal on Optimization
Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Simple Bounds and Equality Constraints

SIAM Journal on Optimization
An algorithm for the numerical realization of 3D contact problems with Coulomb friction

Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Minimizing quadratic functions subject to bound constraints with the rate of convergence and finite termination

Computational Optimization and Applications

An Optimal Algorithm for Minimization of Quadratic Functions with Bounded Spectrum Subject to Separable Convex Inequality and Linear Equality Constraints

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Original article: Approximation and numerical realization of 3D quasistatic contact problems with Coulomb friction

Mathematics and Computers in Simulation

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Abstract

This article deals with minimizing quadratic functions with a special form of quadratic constraints that arise in 3D contact problems of linear elasticity with isotropic friction [Haslinger, J., Kucera, R. and Dostál, Z., 2004, An algorithm for the numerical realization of 3D contact problems with Coulomb friction. Journal of Computational and Applied Mathematics, 164/165, 387-408.]. The proposed algorithm combines the active set method with the conjugate gradient method. Its general scheme is similar to the algorithms of Polyak's type that solve the quadratic programming problems with simple bounds. As the algorithm does not terminate in a finite number of steps, the convergence is proved. The implementation uses an adaptive precision control of the conjugate gradient loops. Numerical experiments demonstrate the computational efficiency of the method.