论文信息 - On the convergence of sequential minimization algorithms

On the convergence of sequential minimization algorithms

This note discusses the conditions for convergence of algorithms for finding the minimum of a function of several variables which are based on solving a sequence of one-variable minimization problems. Theorems are given which contrast the weakest conditions for convergence of gradient-related algorithms with those for more general algorithms, including those which minimize in turn along a sequence of uniformly linearly independent search directions.

R. Sargent | D. Sebastian

[1] H. H. Rosenbrock,et al. An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[2] M. J. D. Powell,et al. An efficient method for finding the minimum of a function of several variables without calculating derivatives , 1964, Comput. J..

[3] A. A. Goldstein,et al. Minimizing Functionals on Normed-Linear Spaces , 1966 .

[4] L. Armijo. Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[5] Willard I. Zangwill,et al. Minimizing a function without calculating derivatives , 1967, Comput. J..

[6] A. Ostrowski. Solution of equations and systems of equations , 1967 .

[7] P. Wolfe. Convergence Conditions for Ascent Methods. II , 1969 .

[8] Bruce A. Murtagh,et al. Computational Experience with Quadratically Convergent Minimisation Methods , 1970, Comput. J..

[9] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[10] B. V. Shah,et al. Integer and Nonlinear Programming , 1971 .

[11] E. Polak,et al. Computational methods in optimization : a unified approach , 1972 .

[12] M. J. D. Powell,et al. On search directions for minimization algorithms , 1973, Math. Program..