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A Trajectory-Based Method for Constrained Nonlinear Optimization Problems

  • M. Montaz Ali
  • Terry-Leigh Oliphant
Article
  • 151 Downloads

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 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer Science and Applied MathematicsUniversity of the Witwatersrand (Wits)JohannesburgSouth Africa
  2. 2.TCSE, Faculty of Engineering and Built EnvironmentUniversity of the Witwatersrand (Wits)JohannesburgSouth Africa

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