Abstract
The continuation method known for the numerical solution of nonlinear equations is applied to nonlinear optimization problems with constraints. Moving along the homotopy path, only the active constraints are considered. We assume that there exists only a finite number of critical points, i.e. points where the index set of the active constraints changes. Then a theoretic concept of a globally convergent algorithm consists of the following three phases:
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1.
Inside a stability set the solution is computed by help of classical continuation.
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2.
At the boundary of a stability set a critical point t has to be determined.
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3.
Passing t, the new active index set must be identified.
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Gfrerer, H., Guddat, J., Wacker, H., Zulehner, W. (1983). Globalization of Locally Convergent Algorithms for Nonlinear Optimization Problems with Constraints. In: Fiacco, A.V., Kortanek, K.O. (eds) Semi-Infinite Programming and Applications. Lecture Notes in Economics and Mathematical Systems, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46477-5_9
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DOI: https://doi.org/10.1007/978-3-642-46477-5_9
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