Abstract
The four most important approaches for solving the constrained nonlinear programming problem, are the penalty, multiplier, sequential quadratic programming, and generalized reduced gradient method. A general algorithmic frame will be presented, which realizes any of these methods only by specifying a search direction for the variables, a multiplier estimate, and some penalty parameters in each iteration. This approach allows to illustrate common mathematical features and, on the other hand, serves to explain the different numerical performance results we observe in practice. It will be shown that the algorithm is well-defined and approximates a Kuhn-Tucker point of the underlying problem.
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© 1984 Springer-Verlag
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Schittkowski, K. (1984). A unified nonlinear programming theory for penalty, multiplier, SQP and GRG methods. In: Thoft-Christensen, P. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 59. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008903
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DOI: https://doi.org/10.1007/BFb0008903
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