A method of analytic centers for quadratically constrained convex quadratic programs
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Matrix computations (3rd ed.)
Trust-region methods
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Box Constrained Quadratic Programming with Proportioning and Projections
SIAM Journal on Optimization
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
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)
Computational Optimization and Applications
Minimizing quadratic functions with separable quadratic constraints
Optimization Methods & Software
SIAM Journal on Optimization
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
A scalable TFETI algorithm for two-dimensional multibody contact problems with friction
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
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An, in a sense, optimal algorithm for minimization of quadratic functions subject to separable convex inequality and linear equality constraints is presented. Its unique feature is an error bound in terms of bounds on the spectrum of the Hessian of the cost function. If applied to a class of problems with the spectrum of the Hessians in a given positive interval, the algorithm can find approximate solutions in a uniformly bounded number of simple iterations, such as matrix-vector multiplications. Moreover, if the class of problems admits a sparse representation of the Hessian, it simply follows that the cost of the solution is proportional to the number of unknowns. Theoretical results are illustrated by numerical experiments.