A Trajectory-Based Method for Constrained Nonlinear Optimization Problems

M. Montaz Ali and Terry-Leigh Oliphant ()
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M. Montaz Ali: University of the Witwatersrand (Wits)
Terry-Leigh Oliphant: University of the Witwatersrand (Wits)

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 2, No 10, 479-497

Abstract: 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.

Keywords: Trajectory-based method; Constrained nonlinear optimization; System of ordinary differential equations; Numerical integration; Convergence (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1274-9

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