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A globally convergent primal-dual active-set framework for large-scale convex quadratic optimization

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  • Frank Curtis
  • Zheng Han
  • Daniel Robinson

Abstract

We present a primal-dual active-set framework for solving large-scale convex quadratic optimization problems (QPs). In contrast to classical active-set methods, our framework allows for multiple simultaneous changes in the active-set estimate, which often leads to rapid identification of the optimal active-set regardless of the initial estimate. The iterates of our framework are the active-set estimates themselves, where for each a primal-dual solution is uniquely defined via a reduced subproblem. Through the introduction of an index set auxiliary to the active-set estimate, our approach is globally convergent for strictly convex QPs. Moreover, the computational cost of each iteration typically is only modestly more than the cost of solving a reduced linear system. Numerical results are provided, illustrating that two proposed instances of our framework are efficient in practice, even on poorly conditioned problems. We attribute these latter benefits to the relationship between our framework and semi-smooth Newton techniques. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Frank Curtis & Zheng Han & Daniel Robinson, 2015. "A globally convergent primal-dual active-set framework for large-scale convex quadratic optimization," Computational Optimization and Applications, Springer, vol. 60(2), pages 311-341, March.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:2:p:311-341
    DOI: 10.1007/s10589-014-9681-9
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    Cited by:

    1. Enrico Bettiol & Lucas Létocart & Francesco Rinaldi & Emiliano Traversi, 2020. "A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs," Computational Optimization and Applications, Springer, vol. 75(2), pages 321-360, March.
    2. Oleg Burdakov & Oleg Sysoev, 2017. "A Dual Active-Set Algorithm for Regularized Monotonic Regression," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 929-949, March.
    3. Jean-Pierre Dussault & Mathieu Frappier & Jean Charles Gilbert, 2019. "A lower bound on the iterative complexity of the Harker and Pang globalization technique of the Newton-min algorithm for solving the linear complementarity problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 359-380, December.
    4. Assalé Adjé, 2021. "Quadratic Maximization of Reachable Values of Affine Systems with Diagonalizable Matrix," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 136-163, April.

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