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Pseudotransient Continuation for Solving Systems of Nonsmooth Equations with Inequality Constraints

Author

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  • J. Chen

    (University of Colorado Denver)

  • L. Qi

    (The Hong Kong Polytechnic University)

Abstract

This paper investigates a pseudotransient continuation algorithm for solving a system of nonsmooth equations with inequality constraints. We first transform the inequality constrained system of nonlinear equations to an augmented nonsmooth system, and then employ the pseudotransient continuation algorithm for solving the corresponding augmented nonsmooth system. The method gets its global convergence properties from the dynamics, and inherits its local convergence properties from the semismooth Newton method. Finally, we illustrate the behavior of our approach by some numerical experiments.

Suggested Citation

  • J. Chen & L. Qi, 2010. "Pseudotransient Continuation for Solving Systems of Nonsmooth Equations with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 223-242, November.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:2:d:10.1007_s10957-010-9719-9
    DOI: 10.1007/s10957-010-9719-9
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    References listed on IDEAS

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    1. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    2. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
    3. X. J. Tong & L. Qi, 2004. "On the Convergence of a Trust-Region Method for Solving Constrained Nonlinear Equations with Degenerate Solutions," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 187-211, October.
    4. L. Qi & X. J. Tong & D. H. Li, 2004. "Active-Set Projected Trust-Region Algorithm for Box-Constrained Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 601-625, March.
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