A Trajectory-Based Method for Constrained Nonlinear Optimization Problems

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 augm...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 177; no. 2; pp. 479 - 497
Main Authors Ali, M. Montaz, Oliphant, Terry-Leigh
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Differential equations
Engineering
Mathematics
Mathematics and Statistics
Nonlinear programming
Numerical integration
Operations Research/Decision Theory
Optimization
Optimization algorithms
Parameters
Theory of Computation
Trajectory optimization
System of ordinary differential equations
Numerical integration
Trajectory-based method
Constrained nonlinear optimization
Convergence
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1274-9