Bound constrained quadratic programming via piecewise

Kaj Madsen, Hans Bruun Nielsen, M. C. Pinar

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    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 lambda/sub 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 lambda/sub 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.
    Original languageEnglish
    JournalMath. Prog.
    Volume85
    Issue number1
    Pages (from-to)135-156
    ISSN0025-5610
    Publication statusPublished - 1999

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