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functionsHMIP.m
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classdef functionsHMIP
properties
activation_type='sin'
beta=1;
size=1;
end
methods
function funcs=functionsHMIP
if funcs.beta==1
funcs.beta=ones(funcs.size,1);
end
end
function out=activation(funcs,x,lb,ub)
if nargin==2
lb=zeros(funcs.size,1);
ub=ones(funcs.size,1);
end
y=(x-lb)./(ub-lb);
if strcmp(funcs.activation_type,'tanh')
out=0.5*(tanh(2*funcs.beta.*(y-0.5))+1);
elseif strcmp(funcs.activation_type,'pwl')
out=funcs.box_projection(funcs.beta.*(y-0.5)+0.5,0,1);
elseif strcmp(funcs.activation_type,'sin')
out=(0.5*sin(2*funcs.beta.*(y-0.5))+0.5).*(0.5-pi./(4*funcs.beta)<y).*(y<0.5+pi./(4 *funcs.beta))+(y>=0.5+pi./(4*funcs.beta));
elseif strcmp(funcs.activation_type,'identity')
out=y;
end
out=(ub-lb).*out+lb;
end
function out=proxy_distance_activation(funcs,x,lb,ub)
if nargin==2
lb=zeros(funcs.size,1);
ub=ones(funcs.size,1);
end
if strcmp(funcs.activation_type,'tanh')
out=(4./((ub-lb).^2)).*funcs.beta.*(x-lb).*(ub-x);
elseif strcmp(funcs.activation_type,'pwl')
out=funcs.beta.*(x~=ub).*(x~=lb);
elseif strcmp(funcs.activation_type,'sin')
out=2./(ub-lb).*funcs.beta.*sqrt((x-lb).*(ub-x));
elseif strcmp(funcs.activation_type,'identity')
out=1;
end
end
function out=inverse_activation(funcs,x,lb,ub)
if nargin==2
lb=zeros(funcs.size,1);
ub=ones(funcs.size,1);
end
y=(x-lb)./(ub-lb);
if strcmp(funcs.activation_type,'tanh')
out=(1./(2*funcs.beta)).*atanh(2.*(y-0.5))+0.5;
elseif strcmp(funcs.activation_type,'pwl')
out=(1./funcs.beta).*(y-0.5)+0.5;
elseif strcmp(funcs.activation_type,'sin')
out=(1./(2*funcs.beta)).*asin(2.*(y-0.5))+0.5;
elseif strcmp(funcs.activation_type,'identity')
out=y;
end
out=(ub-lb).*out+lb;
end
end
methods(Static)
function [H,h,cst]=quadratic_model(fun,grad_fun,x_0,epsilon)
n=length(grad_fun(x_0));
x_0=x_0.*ones(n,1);
E=eye(n);
H=NaN*zeros(n,n);
grad_0=grad_fun(x_0);
for i=1:n
h=(1/epsilon)*(grad_fun(x_0+epsilon*E(:,i))-grad_0);
H(:,i)=h;
end
H=0.5*(H+H');
m=min(eig(H));
if m<0
H=H-m*eye(n);
end
h=grad_0-H*x_0;
cst=fun(x_0)-0.5*x_0'*H*x_0-h'*x_0;
end
function [H,h,cst,x,f_val]=quadratic_model_bfgs(fun,grad_fun,x_0,num)
if nargin==3
num=10^3;
end
n=length(grad_fun(x_0));
x=NaN*zeros(n,num+1);
x(:,1)=x_0.*ones(n,1);
delta_x=NaN*zeros(n,num);
y=NaN*zeros(n,num);
inv_H=0.01*eye(n);
iter=1;
var_x=1;
gradient=grad_fun(x(:,1));
new_gradient=gradient;
while iter<num && norm(var_x,'Inf')>10^(-6) && norm(new_gradient)>10^-6
gradient=new_gradient;
delta_x(:,iter)=-0.5*inv_H*gradient;
x(:,iter+1)=x(:,iter)+delta_x(:,iter);
new_gradient=grad_fun(x(:,iter+1));
y(:,iter)=new_gradient-gradient;
denominator=delta_x(:,iter)'*y(:,iter);
if abs(denominator)>10^-9
inv_H=(eye(n)-delta_x(:,iter)*y(:,iter)'/denominator)*inv_H*(eye(n)-y(:,iter)*delta_x(:,iter)'/denominator)+delta_x(:,iter)*delta_x(:,iter)'/denominator;
end
var_x=norm(delta_x(:,iter),'Inf');
iter=iter+1;
end
x=x(:,iter);
H=round(inv(inv_H+10^(-6)*eye(n)),6);
h=round(new_gradient-H*x,6);
cst=round(fun(x)-0.5*x'*H*x-h'*x,6);
f_val=fun(x);
end
function out=box_projection(x,lb,ub)
out=max(lb,min(x,ub));
end
function out=is_in_box(x,lb,ub)
if max(lb,min(x,ub))==x
out=true;
else
out=false;
end
end
function smoothness_val=compute_approximate_smoothness_coef(gradient,lb,ub,n)
n_rand=100*log(n);
smoothness_val=0;
for k=1:n_rand
point_1=(ub-lb).*rand(n,1)+lb;
point_2=(ub-lb).*rand(n,1)+lb;
distance=norm(point_1-point_2);
if distance>10^(-6)
smoothness_val=max(smoothness_val,norm(gradient(point_1)-gradient(point_2))/distance);
end
end
end
function z=normalize(x)
if norm(x)>0
z=x/norm(x);
else
z=zeros(length(x),1);
end
end
function out=binary_cv(x,binary_index)
z=x.*binary_index;
out=sum(min(abs(z),abs(1-z)));
out=out/sum(binary_index);
end
end
end