caa a22 4500 467948410 CHVBK 20180405193739.0 cr unu---uuuuu 170328e20050101xx s 000 0 eng 10.1007/s10589-005-4557-7 doi (NATIONALLICENCE)springer-10.1007/s10589-005-4557-7 (NATIONALLICENCE)springer-10.1023/B:COAP.0000049888.80264.25 Minimizing Quadratic Functions Subject to Bound Constraints with the Rate of Convergence and Finite Termination [Elektronische Daten] [Zdeněk Dostál, Joachim Schöberl] A new active set based algorithm is proposed that uses the conjugate gradient method to explore the face of the feasible region defined by the current iterate and the reduced gradient projection with the fixed steplength to expand the active set. The precision of approximate solutions of the auxiliary unconstrained problems is controlled by the norm of violation of the Karush-Kuhn-Tucker conditions at active constraints and the scalar product of the reduced gradient with the reduced gradient projection. The modifications were exploited to find the rate of convergence in terms of the spectral condition number of the Hessian matrix, to prove its finite termination property even for problems whose solution does not satisfy the strict complementarity condition, and to avoid any backtracking at the cost of evaluation of an upper bound for the spectral radius of the Hessian matrix. The performance of the algorithm is illustrated on solution of the inner obstacle problems. The result is an important ingredient in development of scalable algorithms for numerical solution of elliptic variational inequalities. Springer Science+Business Media, Inc., 2005 quadratic programming nationallicence bound constraints nationallicence inexact active set strategy nationallicence rate of convergence nationallicence finite termination nationallicence Dostál Zdeněk FEI VŠB-Technical University Ostrava, Tř 17 listopadu, CZ-70833, Ostrava, Czech Republic aut Schöberl Joachim Department of Mathematics, Johannes Kepler University, A-4040, Linz, Austria aut Computational Optimization and Applications Kluwer Academic Publishers 30/1(2005-01-01), 23-43 0926-6003 30:1<23 2005 30 10589 https://doi.org/10.1007/s10589-005-4557-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10589-005-4557-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dostál Zdeněk FEI VŠB-Technical University Ostrava, Tř 17 listopadu, CZ-70833, Ostrava, Czech Republic aut NATIONALLICENCE 700 1- Schöberl Joachim Department of Mathematics, Johannes Kepler University, A-4040, Linz, Austria aut NATIONALLICENCE 773 0- Computational Optimization and Applications Kluwer Academic Publishers 30/1(2005-01-01), 23-43 0926-6003 30:1<23 2005 30 10589 NATIONALLICENCE 700 1- Dostal Zdenek FEI VSB-Technical University Ostrava, Tr 17listopadu, CZ-70833, Ostrava, Czech Republic aut NATIONALLICENCE 700 1- Schoberl Joachim Department of Mathematics, Johannes Kepler University, A-4040, Linz, Austria aut NATIONALLICENCE 856 40 https://doi.org/10.1023/B:COAP.0000049888.80264.25 text/html Onlinezugriff via DOI Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE NATIONALLICENCE NL-springer