% Runs various limited-memory solvers on 2D rosenbrock function for 25

% function evaluations

maxFunEvals = 25;

fprintf('Result after %d evaluations of limited-memory solvers on 2D rosenbrock:\n',maxFunEvals);

fprintf('---------------------------------------\n');

fprintf('x1 = %.4f, x2 = %.4f (starting point)\n',0,0);

fprintf('x1 = %.4f, x2 = %.4f (optimal solution)\n',1,1);

fprintf('---------------------------------------\n');

if exist('minimize') == 2

    % Minimize.m - conjugate gradient method

    x = minimize([0 0]', 'rosenbrock', -maxFunEvals);

    fprintf('x1 = %.4f, x2 = %.4f (minimize.m by C. Rasmussen)\n',x(1),x(2));

end

options = [];

options.display = 'none';

options.maxFunEvals = maxFunEvals;

% Steepest Descent

options.Method = 'sd';

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with steepest descent)\n',x(1),x(2));

% Cyclic Steepest Descent

options.Method = 'csd';

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with cyclic steepest descent)\n',x(1),x(2));

% Barzilai & Borwein

options.Method = 'bb';

options.bbType = 1;

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with spectral gradient descent)\n',x(1),x(2));

% Hessian-Free Newton

options.Method = 'newton0';

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with Hessian-free Newton)\n',x(1),x(2));

% Hessian-Free Newton w/ L-BFGS preconditioner

options.Method = 'pnewton0';

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with preconditioned Hessian-free Newton)\n',x(1),x(2));

% Conjugate Gradient

options.Method = 'cg';

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with conjugate gradient)\n',x(1),x(2));

% Scaled conjugate Gradient

options.Method = 'scg';

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with scaled conjugate gradient)\n',x(1),x(2));

% Preconditioned Conjugate Gradient

options.Method = 'pcg';

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with preconditioned conjugate gradient)\n',x(1),x(2));

% Default: L-BFGS (default)

options.Method = 'lbfgs';

x = minFunc(@rosenbrock,[0 0]',options);

fprintf('x1 = %.4f, x2 = %.4f (minFunc with limited-memory BFGS - default)\n',x(1),x(2));

fprintf('---------------------------------------\n');