Bound constrained quadratic programming via piecewise quadratic functions
Nielsen, H. B.
Pınar, M. Ç.
Mathematical Programming, Series B
135 - 156
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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 λ1 , 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 λ1, 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. © Springer-Verlag 1999.
KeywordsBound constrained quadratic programming
Condition estimation Newton iteration factorization update