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Optimization_algo.m
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classdef Optimization_algo
%UNTITLED2 Summary of this class goes here
% Detailed explanation goes here
properties
f %test_function object
l % learning rate
eps %tolerance for stopping
n % maximum number of iterations
plot_
animate
a
function_values
end
methods
function obj = Optimization_algo(f,l,eps,n,p,animate)
obj.f=f;
obj.l=l;
obj.eps=eps;
obj.plot_=p;
obj.animate = animate;
obj.n = n;
if obj.plot_
obj.function_values = [];
end
if obj.animate
obj.a = Plot(obj.f);
%obj.a.graph();
figure()
end
end
function x1 = Gradient_descent(obj,x0)
%UNTITLED2 Construct an instance of this class
% Detailed explanation goes here
x1 = x0;
for i=1:obj.n
disp(obj.f.eval(x0))
gradient = obj.f.grad(x0);
temp =x1;
x1 = x0 - obj.l*gradient;
x0 =temp;
if norm(gradient) <= obj.eps
break
end
if obj.animate
obj.a.call(x0,x1,'Gradient Descent')
end
if obj.plot_
obj.function_values = [obj.function_values obj.f.eval(x0)];
end
end
if obj.plot_
figure()
plot(1:numel(obj.function_values),obj.function_values)
title('Gradient Descent')
xlabel ('Time')
ylabel('f(x)')
end
end
function x1 = Momentum(obj,x0,alpha)
%UNTITLED2 Construct an instance of this class
% Detailed explanation goes here
x1 = x0;
m = zeros(1,obj.f.dim);
for i=1:obj.n
disp(obj.f.eval(x0))
gradient = obj.f.grad(x0);
m = alpha*m + obj.l*gradient;
temp =x1;
x1 = x0 - m;
x0 = temp;
if norm(gradient) <= obj.eps
break
end
if obj.animate
obj.a.call(x0,x1,'Momentum')
end
if obj.plot_
obj.function_values = [obj.function_values obj.f.eval(x0)];
end
end
if obj.plot_
figure()
plot(1:numel(obj.function_values),obj.function_values)
title('Momentum')
xlabel ('Time')
ylabel('f(x)')
end
end
function x1 = NesterovMomentum(obj,x0,alpha)
%UNTITLED2 Construct an instance of this class
% Detailed explanation goes here
x1 = x0;
m = zeros(1,obj.f.dim);
for i=1:obj.n
disp(obj.f.eval(x0))
gradient = obj.f.grad(x0-alpha*m); %lookahead gradient
m = alpha*m + obj.l*gradient;
temp =x1;
x1 = x0 - m;
x0 = temp;
if norm(gradient) <= obj.eps
break
end
if obj.animate
obj.a.call(x0,x1,'NesterovMomentum')
end
if obj.plot_
obj.function_values = [obj.function_values obj.f.eval(x0)];
end
end
if obj.plot_
figure()
plot(1:numel(obj.function_values),obj.function_values)
title('NesterovMomentum')
xlabel ('Time')
ylabel('f(x)')
end
end
function x1 = AdaGrad(obj,x0)
%UNTITLED2 Construct an instance of this class
% Detailed explanation goes here
x1 = x0;
G = zeros(1,obj.f.dim);
for i=1:obj.n
disp(obj.f.eval(x0))
gradient = obj.f.grad(x0);
G = G + gradient.^2;
temp = x1;
x1 = x0 - obj.l*gradient./sqrt(G+0.1^15);
x0 = temp;
if norm(gradient) <= obj.eps
break
end
if obj.animate
obj.a.call(x0,x1,'AdaGrad')
end
if obj.plot_
obj.function_values = [obj.function_values obj.f.eval(x0)];
end
end
if obj.plot_
figure()
plot(1:numel(obj.function_values),obj.function_values)
title('AdaGrad')
xlabel ('Time')
ylabel('f(x)')
end
end
function x1 = RMSprop(obj,x0,alpha)
%UNTITLED2 Construct an instance of this class
% Detailed explanation goes here
x1 = x0;
G = zeros(1,obj.f.dim);
for i=1:obj.n
disp(obj.f.eval(x0))
disp(i)
gradient = obj.f.grad(x0);
G = alpha*G + (1-alpha)*gradient.^2;
temp = x1;
x1 = x0 - obj.l*gradient./sqrt(G+0.1^15);
x0 = temp;
if norm(gradient) <= obj.eps
break
end
if obj.animate
obj.a.call(x0,x1,'RMSprop')
end
if obj.plot_
obj.function_values = [obj.function_values obj.f.eval(x0)];
end
end
if obj.plot_
figure()
plot(1:numel(obj.function_values),obj.function_values)
title('RMSprop')
xlabel ('Time')
ylabel('f(x)')
end
end
function x1 = Adam(obj,x0,beta1,beta2)
%UNTITLED2 Construct an instance of this class
% Detailed explanation goes here
x1 = x0;
G = zeros(1,obj.f.dim);
m = zeros(1,obj.f.dim);
for i=1:obj.n
disp(obj.f.eval(x0))
disp(i)
gradient = obj.f.grad(x0);
G = (beta2*G + (1-beta2)*gradient.^2)/(1-beta2^i);
m = (beta1*m + (1-beta1)*obj.l*gradient)/(1-beta1^i);
temp = x1;
x1 = (x0 - obj.l*m)./(sqrt(G)+0.1^8);
x0 = temp;
if norm(gradient) <= obj.eps
break
end
if obj.animate
obj.a.call(x0,x1,'Adam')
end
if obj.plot_
obj.function_values = [obj.function_values obj.f.eval(x0)];
end
end
if obj.plot_
figure()
plot(1:numel(obj.function_values),obj.function_values)
title('Adam')
xlabel ('Time')
ylabel('f(x)')
end
end
end
end