stepsize_wolfe_powell.m

function [t_opt,nr_fct,nr_grad]=stepsize_wolfe_powell (model, x, d);
%function [t_opt,nr_fct,nr_grad]=stepsize_wolfe_powell (model, x, d)
%
% Function calculating a stepsize following the Wolfe-Powell-rule
%
%Required fields of model:
% model.optimization.get_Jacobian: gradient function
% model.optimization.objective_function: function to be optimized
% x: initial value
% d: search direction
%
%
%Output variables
% t_opt: optimal value for stepsize t
% nr_fct: number of function calls needed during process
% nr_grad: number of calculations of the gradient
%
%
% Oliver Zeeb 20.05.2010%


nr_fct = 0; %counter for number of function calls
nr_grad = 0; %counter for number of gradient calculations

rho = 0.25;     % 0 < rho < 0.5
sigma = 0.125;  % 0 < sigma < 0.5

grad_f = model.optimization.get_Jacobian;
func = model.optimization.objective_function;



%needed functions for the algorithm
grad_phi_0 = grad_f(x)*d'; 
nr_grad=nr_grad+1;

phi = @(t) func(x+t*d); 
psi = @(t) phi(t) - phi(0) - sigma*t*grad_phi_0;

grad_phi = @(t) grad_f(x+t*d)*d';

t=1;
phi_test=func(x+t*d);
psi_test=phi(t) - phi(0) - sigma*t*grad_phi_0;
grad_ohi_test=grad_f(x+t*d)*d';


%
% Phase A
%

kondition_a = 0; % condition, to enter the Phase-A-loop

% (A.0)
t=1;
gamma=2;

% (A.1)
while kondition_a == 0
    nr_fct=nr_fct+1; % checking the next if-condition needs a function call
    if psi(t) >= 0
        a=0;
        b=t;
        kondition_a = 1;
        break;                              % leaving this loop, continuing with Phase B
    elseif grad_phi(t) >= rho*grad_phi_0    % psi(t) < 0 and phi_strich(t) >= rho * phi_strich(0) --> algorithm found an optimal stepsize t
        nr_grad=nr_grad+1;
        t_opt=t;
        return          % STOP 1 
    else      % psi(t) < 0 an phi_strich(t) < rho * phi_strich(0)
       nr_grad=nr_grad+1; %grad_phi in elseif condition needed calculation of the gradient
       t=gamma*t;
    end
end


%
% Phase B
%

% (B.0)
tau1 = 0.2;       % 0 < tau1 < 0.5
tau2 = 0.2;       % 0 < tau2 < 0.5

kondition_b=0; % condition to enter the Phase-B-loop

% According to the Wolfe-Powell-Algorithm the following loop terminates
while kondition_b == 0
    % (B.1)
    t=0.5*(a*(1-tau1+tau2) + b*(1+tau1-tau2)); % choose t in [a+tau1(b-a), b-tau2(b-a)
    
    % (B.2)
    nr_fct=nr_fct+1; %checking the next if-condition needs a function call
    if psi(t) >= 0
        b=t;
    elseif grad_phi(t) >= rho * grad_phi_0 % psi(t) > 0 and phi_strich(t) >= rho* phi_strich(0) --> algorithm found an optimal stepsize t
        nr_grad=nr_grad+1;
        t_opt=t;
        return % STOP 2 point where the algorithm terminates! --> leaves the function
    else     % psi(t) < 0 and phi_strich(t) < rho * phi_strich(0)
        nr_grad=nr_grad+1; %grad_phi in elseif condition needed calculation of the gradient
        a=t;
    end

end