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opt03_run.m
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213 lines (209 loc) · 6.75 KB
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%% OPT03_RUN
%
% Discussion:
%
% This problem includes a parameter P that the user must set
% in order to complete the definition of the problem.
%
% Except when P = 8, the minimized value of F is nonzero. This
% can cause problems for the Gauss-Newton method.
%
% Modified:
%
% 10 January 2008
%
%---------------------------------------------------------------------
% Running testcase, from D+S, pp. 225-6, 231;
%---------------------------------------------------------------------
fprintf('---------------------------------------------------------\n')
fprintf('NEWTON applied to F,G,H optimization system:\n')
fname = 'opt03_fgh';
options = [];
options.verbose = 0;
options.method = 'newton';
options.step_tolerance = 1.e-15;
options.globalization = 'none';
options.gradient_tolerance = 1.e-10;
options.max_iterations = 40;
%
% This run should require about 7 iterations.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = 8;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Newton produced (%10.7e)\n',x(1))
f = opt03_fgh ( x, 'f', p );
fprintf('Value of F(X) = %10.7e\n\n', f );
%
% This run should require about 9 iterations.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = 3;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Newton produced (%10.7e)\n',x(1))
f = opt03_fgh ( x, 'f', p );
fprintf('Value of F(X) = %10.7e\n\n', f );
%
% This run should require about 10 iterations.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = -1;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Newton produced (%10.7e)\n',x(1))
f = opt03_fgh ( x, 'f', p );
fprintf('Value of F(X) = %10.7e\n\n', f );
%
% This run should require about 12 iterations.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = -4;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Newton produced (%10.7e)\n',x(1))
f = opt03_fgh ( x, 'f', p );
fprintf('Value of F(X) = %10.7e\n\n', f );
%
% This run should require about 12 iterations.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = -8;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Newton produced (%10.7e)\n',x(1))
f = opt03_fgh ( x, 'f', p );
fprintf('Value of F(X) = %10.7e\n\n', f );
%
% This run should require about 5 iterations.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = 3;
x0 = [.5];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Newton produced (%10.7e)\n',x(1))
f = opt03_fgh ( x, 'f', p );
fprintf('Value of F(X) = %10.7e\n\n', f );
%---------------------------------------------------------------------
% Running testcase, from D+S, pp. 225-6, 231;
% This is used to test Gauss-Newton strategies.
%---------------------------------------------------------------------
fprintf('---------------------------------------------------------\n')
fprintf('Gauss-Newton applied to RES, JAC nonlinear least squares system: \n')
fname = 'opt03_rj';
options = [];
options.verbose = 0;
options.method = 'gauss_newton';
options.step_tolerance = 1.e-15;
options.globalization = 'none';
options.gradient_tolerance = 1.e-10;
options.max_iterations = 40;
%
% This run should require about 12 iterations.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = 8;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Gauss Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Gauss-Newton produced (%10.7e)\n',x(1))
[ res, jac ] = opt03_rj ( x, 'f', p );
fprintf('Norm of RES(X) = %10.7e\n\n', norm ( res ) );
%
% This run should require about 12 iterations.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = 3;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Gauss Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Gauss-Newton produced (%10.7e)\n',x(1))
[ res, jac ] = opt03_rj ( x, 'f', p );
fprintf('Norm of RES(X) = %10.7e\n\n', norm ( res ) );
%
% This run should not converge
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = -1;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Gauss Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Gauss-Newton produced (%10.7e)\n',x(1))
[ res, jac ] = opt03_rj ( x, 'f', p );
fprintf('Norm of RES(X) = %10.7e\n\n', norm ( res ) );
%
% This run should not converge.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = -4;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Gauss Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Gauss-Newton produced (%10.7e)\n',x(1))
[ res, jac ] = opt03_rj ( x, 'f', p );
fprintf('Norm of RES(X) = %10.7e\n\n', norm ( res ) );
%
% This run should not converge.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = -8;
x0 = [1];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Gauss Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Gauss-Newton produced (%10.7e)\n',x(1))
[ res, jac ] = opt03_rj ( x, 'f', p );
fprintf('Norm of RES(X) = %10.7e\n\n', norm ( res ) );
%
% This run should require about 9 steps.
%
fprintf('---------------------------------------------------------\n')
fprintf ( '\n' );
p = 3;
x0 = [.5];
fprintf ( ' Start X0 = %f\n', x0 );
fprintf ( ' Parameter P = %f\n', p );
fprintf('Gauss Newton:\n')
x = entrust ( fname, x0, options, p );
fprintf('Gauss-Newton produced (%10.7e)\n',x(1))
[ res, jac ] = opt03_rj ( x, 'f', p );
fprintf('Norm of RES(X) = %10.7e\n', norm ( res ) );