A modularized package of dual algorithms for solving constrained nonlinear programming problems

A package of algorithms for numerical experimentation with constrained optimization methods is described. This package is addressed to dual methods and is modularized to permit experiments with a particular module (such as a penalty function module) without changing any of the other modules. Thus reliable comparisons can be made without questioning differences in implementations of the remaining portions of a constrained algorithm. The feasibility of modularization as well as advantages and disadvantages for dual algorithms are discussed. Some numerical results are also presented.

[1]  John R. Rice.  On the Construction of Polyalgorithms for Automatic Numerical Analysis , 1968 .

[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]  Garth P. McCormick,et al.  A Guide to SUMT-Version 4: The Computer Program Implementing the Sequential Unconstrained Minimization Technique for Nonlinear Programming, , 1965 .

[4]  Roger Fletcher,et al.  An exact penalty function for nonlinear programming with inequalities , 1973, Math. Program..

[5]  J. B. Rosen,et al.  Construction of nonlinear programming test problems , 1965 .

[6]  R. Brent.  Table errata: Algorithms for minimization without derivatives (Prentice-Hall, Englewood Cliffs, N. J., 1973) , 1975 .

[7]  R. Rockafellar.  Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming , 1974 .

[8]  Thomas John Aird.  Computational solution of global nonlinear least-squares problems. , 1973 .

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

[10]  O. Mangasarian.  Unconstrained Lagrangians in Nonlinear Programming , 1975 .

[11]  William C. Davidon,et al.  Optimally conditioned optimization algorithms without line searches , 1975, Math. Program..

[12]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[13]  J. Ben Rosen,et al.  Pracniques: construction of nonlinear programming test problems , 1965, Commun. ACM.

[14]  John R. Rice,et al.  On the construction of polyalgorithms for automatic numerical analysis , 1967, Symposium on Interactive Systems for Experimental Applied Mathematics.

[15]  Roger Fletcher,et al.  FORTRAN subroutines for minimization by quasi-Newton methods , 1972 .