A Trajectory-Based Method for Constrained Nonlinear Optimization Problems

  • M. Montaz Ali
  • Terry-Leigh Oliphant


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.


Trajectory-based method Constrained nonlinear optimization System of ordinary differential equations Numerical integration Convergence 


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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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