A Trajectory-Based Method for Constrained Nonlinear Optimization Problems |
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| Authors: | M Montaz Ali Terry-Leigh Oliphant |
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| Institution: | 1.School of Computer Science and Applied Mathematics,University of the Witwatersrand (Wits),Johannesburg,South Africa;2.TCSE, Faculty of Engineering and Built Environment,University of the Witwatersrand (Wits),Johannesburg,South Africa |
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| 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. |
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