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Lagrange Efficient and Adaptive Lagrange-Multiplier Methods for Continuous Nonlinear Optimization

By Tao Wang and Benjamin W. Wah


In this paper, we address three important issues in applying Lagrangian methods to solve optimization problems with inequality constraints. First, we propose a MaxQ method that transforms inequality constraints to equality constraints. It overcomes divergence and oscillations that occur in the slack-variable method. Some strategies to speed up its convergence are also examined. Second, we develop a method to monitor the balance between descents in the originalvariable space and ascents in the Lagrange-multiplier space in Lagrangian methods. During the search, we adjust this balance adaptively in order to improve convergence speed. Third, we introduce a nonlinear traveling trace to pull a search trajectory out of a local equilibrium point in a continuous fashion without restarting the search and without losing information already obtained in the local search. This strategy extends existing Lagrangian methods from a local search of equilibrium points to a global search. We implement thes..

Topics: Lagrange Multiplier method, global optimization, inequality constraint, dynamic weighting, MaxQ method
Year: 1999
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