Abstract
We present a quasi-Newton method for interior points algorithms in nonlinear constrained optimization. It is based on a general approach consisting on the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker Optimality Conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points.
This approach is very strong and efficient, and at each iteration it only requires the solution of two linear systems with the same matrix, instead of Quadratic Programming Subproblems. We discuss about theoretical aspects of the algorithm and its computer implementation.
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© 1992 Springer-Verlag Berlin · Heidelberg
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Herskovits, J., Asquier, J. (1992). Quasi — Newton Interior Points Algorithms for Nonlinear Constrained Optimization. In: Bühler, W., Feichtinger, G., Hartl, R.F., Radermacher, F.J., Stähly, P. (eds) Papers of the 19th Annual Meeting / Vorträge der 19. Jahrestagung. Operations Research Proceedings, vol 1990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77254-2_15
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DOI: https://doi.org/10.1007/978-3-642-77254-2_15
Publisher Name: Springer, Berlin, Heidelberg
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