Abstract
Recently developed Newton and quasi-Newton methods for nonlinear programming possess only local convergence properties. Adopting the concept of the damped Newton method in unconstrained optimization, we propose a stepsize procedure to maintain the monotone decrease of an exact penalty function. In so doing, the convergence of the method is globalized.
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Robinson, S. M.,Perturbed Kuhn-Tucker Points and Rates of Convergence for a Class of Nonlinear-Programming Algorithms, Mathematical Programming, Vol. 7, pp. 1–16, 1974.
Garcia-Palomares, U. M., andMangasarian, O. L.,Superlinearly Convergent Quasi-Newton Algorithms for Nonlinearly Constrained Optimization Problems, Mathematical Programming, Vol. 11, pp. 1–13, 1976.
Han, S. P.,Superlinearly Convergent Variable Metric Algorithms for General Nonlinear Programming Problems, Mathematical Programming, Vol. 11, pp. 263–282, 1976.
Kowalik, J., andOsborne, M. R.,Methods for Unconstrained Optimization Problems, American Elsevier, New York, New York, 1968.
Dem'yanov, V. F., andMalozemov, V. N.,Introduction to Minimax, John Wiley and Sons, New York, New York, 1974.
Daniel, J. M.,Stability of the Solution of Definite Quadratic Programs, Mathematical Programming, Vol. 5, pp. 41–53, 1973.
Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.
Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions, I, Springer-Verlag, Berlin, Germany, 1970.
Han, S. P.,Dual Variable Metric Methods for Constrained Optimization Problems, SIAM Journal on Control and Optimization, Vol. 15, No. 4, 1977.
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Communicated by M. R. Hestenes
This research was supported in part by the National Science Foundation under Grant No. ENG-75-10486.
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Han, S.P. A globally convergent method for nonlinear programming. J Optim Theory Appl 22, 297–309 (1977). https://doi.org/10.1007/BF00932858
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DOI: https://doi.org/10.1007/BF00932858