Abstract
In the paper a definition is given of a class of generalized Lagrangians, and some simple properties of them are discussed, especially those related to the topology in the set of constraints. A general formulation of the method of multipliers is presented and a theorem characterising convergence of this method in case of linear-quadratic problems in Hilbert space. Numerical examples of computing the optimal control of time lag systems to terminal functions are presented. The results indicate that the effectiveness of the method of multipliers depends on the choice of the norm in the set of constraints.
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Keywords
- Optimal Control Problem
- Nonlinear Program
- Constraint Violation
- Topological Hausdorff Vector Space
- Surrogate Problem
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Kurcyusz, S. (1976). Some remarks on generalized lagrangians. In: Cea, J. (eds) Optimization Techniques Modeling and Optimization in the Service of Man Part 2. Optimization Techniques 1975. Lecture Notes in Computer Science, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07623-9_299
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DOI: https://doi.org/10.1007/3-540-07623-9_299
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