QPBOX
Bound constrained quadratic programming via piecewise quadratic functions We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of λ 1 , the smallest eigenvalue of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of λ 1 , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive testing and comparison with other methods for constrained QP are given
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References in zbMATH (referenced in 6 articles )
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Sorted by year (- He, Simai; Luo, Zhi-Quan; Nie, Jiawang; Zhang, Shuzhong: Semidefinite relaxation bounds for indefinite homogeneous quadratic optimization (2008)
- Zeng, L. C.; Yao, J. C.: Modified combined relaxation method for general monotone equilibrium problems in Hilbert spaces (2006)
- Li, Wu; de Nijs, J. J.: An implementation of the QSPLINE method for solving convex quadratic programming problems with simple bound constraints. (2003)
- Konnov, Igor V.: A combined relaxation method for a class of nonlinear variational inequalities (2002)
- Mangasarian, O. L.: A finite Newton method for classification (2002)
- Madsen, Kaj; Nielsen, Hans Bruun; Pınar, Mustafa Ç.: Bound constrained quadratic programming via piecewise quadratic functions (1999)