The Davidon-Fletcher-Powell (

This Newton-like behavior of the VMM, as the solution is approached has caused them to be referred as

The DFP method is presented here for historical interest and also the fact it is a little easier to understand than the others.

The improvement of the

Step 1

Step 2

Step 3

The DFP algorithm (A 6.7) is coded in the file. Similar to the previous programs, for two variables the design changes are tracked on a background contour plot. The default initial metric is the identity matrix generated using a MATLAB built in function.DFP.mGoldSection_nVar.m, along withUpperBound_nVar.m,gradfunction.m, and the problem file is also needed.

Usage:DFP('Example6_1',[0.5 0.5],4,0.0001,0,1,20);

>> DFP('Example6_1',[0.5 0.5],4,0.0001,0,1,20);

iteration number: 1

gradient length squared: 2.8411

objective function value: 4.7832

iteration number: 2

gradient length squared: 3.1140e-005

objective function value: 3.0000

The problem: Example6_1

The design vector,function value and KT value

during the iterations

0.5000 0.5000 5.3125 5.2969

0.5996 0.9483 4.7832 2.8411

2.9996 1.9987 3.0000 0.0000

% calling the program

% summary information for program control

% tabular information on the iterations

There are several VMM methods, and you can create your own followingReference 7in this chapter. The most widely used is theBroyden-Fletcher-Goldfarb-Shanno (BFGS)available inSection 6.3.4.