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A Trajectory-Based Method for Constrained Nonlinear Optimization Problems

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  • M. Montaz Ali

    (University of the Witwatersrand (Wits)
    University of the Witwatersrand (Wits))

  • Terry-Leigh Oliphant

    (University of the Witwatersrand (Wits))

Abstract

A trajectory-based method for solving constrained nonlinear optimization problems is proposed. The method is an extension of a trajectory-based method for unconstrained optimization. The optimization problem is transformed into a system of second-order differential equations with the aid of the augmented Lagrangian. Several novel contributions are made, including a new penalty parameter updating strategy, an adaptive step size routine for numerical integration and a scaling mechanism. A new criterion is suggested for the adjustment of the penalty parameter. Global convergence properties of the method are established.

Suggested Citation

  • M. Montaz Ali & Terry-Leigh Oliphant, 2018. "A Trajectory-Based Method for Constrained Nonlinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 479-497, May.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:2:d:10.1007_s10957-018-1274-9
    DOI: 10.1007/s10957-018-1274-9
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    References listed on IDEAS

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    1. S.-P. Han, 1986. "On the Augmented Lagrangian," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 161-168, February.
    2. Ernesto Birgin & J. Martínez, 2012. "Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 941-965, April.
    3. Jean-Philippe Vial & Israel Zang, 1977. "Unconstrained Optimization by Approximation of the Gradient Path," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 253-265, August.
    4. F. Alvarez & A. Cabot, 2004. "Steepest Descent with Curvature Dynamical System," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 247-273, February.
    5. VIAL, Jean-Philippe & ZANG, Israel, 1977. "Unconstrained optimization by approximation of the gradient path," LIDAM Reprints CORE 329, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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