Abstract
The problem of minimizing the maximum residual of a set of non-linear algebraic equations is considered in the case where the functions defining the problem have continuous first derivatives, but no expression for these derivatives is available. The method is based on successive linear approximations of the functions, and solution of the resulting linear systems in the minimax sense subject to bounds on the solutions. Approximations to the matrix of derivatives are updated by using the Broyden [2] rank-one updating formula. It is shown that the method has good convergence properties. Some numerical examples are given.
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References
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© 1975 The Mathematical Programming Society
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Madsen, K. (1975). Minimax solution of non-linear equations without calculating derivatives. In: Balinski, M.L., Wolfe, P. (eds) Nondifferentiable Optimization. Mathematical Programming Studies, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120701
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DOI: https://doi.org/10.1007/BFb0120701
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