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Article

Pospíšil, Lukáš ; Dostál, Zdeněk
Minimization of a convex quadratic function subject to separable conical constraints in granular dynamics. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 175-180
MSC: 65K05, 74M10, 74M15, 90C20, 90C90
Keywords:
constrained optimization; convex quadratic function; granular dynamics; Coulomb friction; modified proportioning with gradient projection; Barzilai-Borwein method
Summary:
The numerical solution of granular dynamics problems with Coulomb friction leads to the problem of minimizing a convex quadratic function with semidefinite Hessian subject to a separable conical constraints. In this paper, we are interested in the numerical solution of this problem. We suggest a modification of an active-set optimal quadratic programming algorithm. The number of projection steps is decreased by using a projected Barzilai-Borwein method. In the numerical experiment, we compare our algorithm with Accelerated Projected Gradient method and Spectral Projected Gradient method on the solution of a particle dynamics problem with hundreds of spherical bodies and static obstacles.
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