
Accession Number : AD0770563
Title : Constrained Multidimensional Minimization without Derivatives. Some Variants of Powell's Method.
Descriptive Note : Final rept. Oct 72Apr 73,
Corporate Author : AIR FORCE ARMAMENT LAB EGLIN AFB FLA
Personal Author(s) : Blowers,James V.
Report Date : JUL 1973
Pagination or Media Count : 168
Abstract : The report discusses two computer versions of Powell's method for minimizing an arbitrary function of several variables with interval constraints without using derivatives. For each code a descriptive algorithm, a list of variables, and several examples are given. The two codes are then extended to cover linear constraints in three ways. All of these include adjusting the penalty functions to fit the linear constraints. In addition to this, the second technique orients the reference directions parallel to the constraints and the third technique projects the successive directions generated by Powell's method onto the constraints during the execution of the body of the algorithm. The third method is thus a hybrid of Powell's method and Rosen's gradient projection method. All of these methods are fast, and none requires derivatives. When these three methods are applied to the two original routines, the result is six new routines. These are applied to an example related to probability of kill problems with varying degrees of success. Again, descriptive algorithms and lists of variables are given. (Author)
Descriptors : *Mathematical programming, *Computer programs, *Functions(Mathematics), Algorithms, Optimization
Subject Categories : Operations Research
Computer Programming and Software
Distribution Statement : APPROVED FOR PUBLIC RELEASE