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q4.py
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import numpy as np
import pandas as pd
def interior_point_method(c,A,b,x0,mu=0.1,tol=0.5,max_iter=500):
x,y = A.shape;
n_var = y;m_equal=x;
x0_prev = x0.reshape(n_var,1);
z0_prev = mu / x0_prev;
z0_prev = z0_prev.reshape((n_var,1));
lambda_par = np.array([0]*m_equal);
lambda_par = lambda_par.reshape((m_equal,1));
val_min = 10**9;
print("shapes x0_prev={} z0_prev={} lambda_par={}".format(x0_prev.shape,z0_prev.shape,lambda_par.shape));
for iter in range(max_iter):
alpha = 1/(10);
X_mat = np.diag(x0_prev.flatten());
Z_mat = np.diag(z0_prev.flatten());
A_derivative = np.zeros((n_var,m_equal));
final_mat = np.zeros((n_var+m_equal,n_var+m_equal));
for i in range(n_var):
for j in range(m_equal):
A_derivative[i][j] = A[j][i];
W_k = np.zeros((n_var,n_var));
for i in range(n_var):
W_k[i][i] = 1/(x0_prev[i][0]**2);
print("shapes X_mat={} Z_mat={} A_derivate={} final_mat={}".format(X_mat.shape,Z_mat.shape,A_derivative.shape,final_mat.shape))
sigma_mat = np.linalg.inv((np.linalg.inv(X_mat))@Z_mat);
new_mat= W_k+sigma_mat;
A_t = A_derivative.T;
for i in range(n_var):
for j in range(n_var):
final_mat[i][j] = new_mat[i][j];
for i in range(0,n_var):
for j in range(n_var,n_var+m_equal):
final_mat[i][j] = A_derivative[i][j-n_var];
for i in range(n_var,n_var+m_equal):
for j in range(0,n_var):
final_mat[i][j] = A_t[i-n_var][j];
inv_mat = np.linalg.inv(final_mat);
c_val = c;
A_org = np.array([0.0]*n_var);
for i in range(m_equal):
A_org += lambda_par[i]*A[i,:];
new_mat_rhs = np.array([0.0]*m_equal);
for i in range(m_equal):
val = A[i,:].reshape((n_var,1)).T@x0_prev.reshape((n_var,1))+b[i];
new_mat_rhs[i] = val;
final_rhs = np.zeros((n_var+m_equal,1));
for i in range(n_var+m_equal):
if(i<n_var):
final_rhs[i][0] = c_val[i]+A_org[i];
else:
final_rhs[i][0] = new_mat_rhs[i-n_var];
result = inv_mat@(-final_rhs);
result = result.reshape((n_var+m_equal,1));
dx = np.zeros((n_var,1));
dy = np.zeros((m_equal,1));
for i in range(n_var+m_equal):
if(i<n_var):
dx[i][0] = result[i][0];
else:
dy[i-n_var][0] = result[i][0];
# dz = np.zeros((n_var,1));
ones_arr = np.ones((n_var,1));
for i in range(m_equal):
z0_prev[i][0] = 0;
final_arr = (mu*(np.linalg.inv(X_mat)@ones_arr))-(z0_prev.reshape((n_var,1)))-(sigma_mat@dx);
dz = final_arr.reshape((n_var,1));
x0_new = x0_prev+alpha*dx;
lambda_new = lambda_par+alpha*dy;
z0_new = z0_prev+alpha*dz;
# print("sum is here",((x0_new-x0_prev)>0).sum());
# print("x0_new={} lambda0_new={} z0_new={}".format(x0_new,lambda_new,z0_new));
val_1=0;
x0_prev = x0_new;
lambda_par = lambda_new;
z0_prev = z0_new;
abb = 0;bcb = 0;
for i in range(n_var):
ab = abs(c_val[i]+A_org[i] - 1/x0_prev[i]);
abb = max(ab,abb);
ones_mat = np.ones((n_var,1));
ones_mat = ones_mat.astype('float');
for i in range(m_equal):
bc = (A[i,:].reshape((n_var,1)).T@x0_prev.reshape((n_var,1))) +b[i];
bcb = max(abs(bc),bcb);
X_mat_new = np.diag(x0_new.flatten());
Z_mat_new = np.diag(z0_new.flatten());
final_const = np.max(np.abs((X_mat_new@(Z_mat_new@ones_mat)) - mu*(ones_mat)));
if(abb<tol and bcb<tol and abs(final_const)<tol):
break;
else:
print("Still here")
print(abb,bcb,final_const);
val_min = min(val_min,10*x0_new[0][0]+9*x0_new[1][0]);
val_opt = val_min;
print("optimal val={}".format(val_opt));
print("decision variable values x0_values={}".format(x0_prev));
# tol constraints;
# Example usage
c = np.array([10, 9,0,0]) # Coefficients of the objective function
# 2x1+3x2;
# A = np.array([[1, 1], [2, -1]]) # Coefficients of the equality constraints
A = np.array([[1,2,3,0],[3,2,0,-1]]);b = np.array([-20,-18]);
# b = np.array([3, 2]) # Right-hand side values of the equality constraints
x0 = np.array([6,0.1,4.5667,0.1]) # Initial guess for the primal variables
# Call the interior point method
# x_optimal = interior_point_method(c, A, b, x0,mu=1)
# # Print the optimal solution
# print("Optimal solution: ", x_optimal)