Some numerical experience with a globally convergent algorithm for nonlinearly constrained optimization

Global convergence properties are established for a quite general form of algorithms for solving nonlinearly constrained minimization problems. A useful feature of the methods considered is that they can be implemented easily either with or without using quadratic programming techniques. A particular implementation, designed to be both efficient and robust, is described in detail. Numerical results are presented and discussed.

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

[2]  M. Powell.  A method for nonlinear constraints in minimization problems , 1969 .

[3]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[4]  John E. Dennis,et al.  On the Local and Superlinear Convergence of Quasi-Newton Methods , 1973 .

[5]  R. Fletcher,et al.  Minimization of a Quadratic Function of Many Variables Subject only to Lower and Upper Bounds , 1974 .

[6]  D. Bertsekas.  Nondifferentiable optimization via approximation , 1975 .

[7]  Shih-Ping Han.  A globally convergent method for nonlinear programming , 1975 .

[8]  R. Fletcher.  An Ideal Penalty Function for Constrained Optimization , 1975 .

[9]  Shih-Ping Han.  Dual variable metric algorithms for constrained optimization , 1975, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[10]  D. Bertsekas,et al.  Combined Primal–Dual and Penalty Methods for Convex Programming , 1976 .

[11]  Ron S. Dembo,et al.  A set of geometric programming test problems and their solutions , 1976, Math. Program..

[12]  Dimitri P. Bertsekas,et al.  Multiplier methods: A survey , 1975, at - Automatisierungstechnik.

[13]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[14]  R. M. Chamberlain,et al.  Some examples of cycling in variable metric methods for constrained minimization , 1979, Math. Program..

[15]  Shih-Ping Han,et al.  Penalty Lagrangian Methods Via a Quasi-Newton Approach , 1979, Math. Oper. Res..