Constrained Multidimensional Minimization without Derivatives. Some Variants of Powell's Method.
Final rept. Oct 72-Apr 73,
AIR FORCE ARMAMENT LAB EGLIN AFB FLA
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The report discusses two computer versions of Powells 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 Powells method onto the constraints during the execution of the body of the algorithm. The third method is thus a hybrid of Powells method and Rosens 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
- Operations Research
- Computer Programming and Software