Browsing by Subject "Bound constrained quadratic programming"

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    Bound constrained quadratic programming via piecewise quadratic functions
    (Springer-Verlag, 1999) Madsen, K.; Nielsen, H. B.; Pınar, M. Ç.
    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.
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    A finite continuation algorithm for bound constrained quadratic programming
    (Society for Industrial and Applied Mathematics Publications, 1998) Madsen, K.; Nielsen, H. B.; Pınar, M. C.
    The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear ℓ1 minimization problem with quadratic terms. A smooth approximation to the linear ℓ1 function is used to obtain a parametric family of piecewise-quadratic approximation problems. The unique path generated by the minimizers of these problems yields the solution to the original problem for finite values of the approximation parameter. Thus, a finite continuation algorithm is designed. Results of extensive computational experiments are reported.