CuttingPlane-Algorithm

Algorithm to run CuttingPlane algorithm in generalized inverses

To run CuttingPlane use (list_g,time_FV) = CuttingPlane(A,r)

Input: a rank-r matrix A as numpy array and the rank r

Output:

• list_g: a list with information about each iteration of the algorithm, as described below:

• list_g[x][0] = Total number of P2 constraints applied

  list_g[x][1] = 1-norm of H

  list_g[x][2] = rank of H (number of singular values greater than 10**(-5))

  list_g[x][3] = Number of elements of H with absolute values greater than 10**(-5)

  list_g[x][4] = Number of elements of R with absolute values greater than 10**(-5) (R = HAA+ - H)

  list_g[x][5] = Percentage of elements of H that satisfy P2.

  list_g[x][6] = Frobenius-norm of R

  list_g[x][7] = Elapsed time to optimize the problem in that specific iteration

• time_FV: total elapsed time to run the algorithm

Example:

import scipy.io

import matplotlib.pyplot as plt

import time

import math

from numpy import linalg as LA

import numpy as np

import gurobipy as gp

from gurobipy import GRB

from sklearn.utils.extmath import randomized_svd

M = scipy.io.loadmat('example.mat')

A= M['A']

r = 10

(list_g,time_FV) = CuttingPlane(A,r)