How to perform operations on cvxopt-matrices a la numpy?

问题

I am working with cvxopt matrices in order to use them in picos library. In general I want to take a matrix, evaluate it on a certain vector, subtract something, then take the biggest absolute value of its entries

import picos as pic
import cvxopt as cvx
import numpy as np

(...)

P = pic.Problem()
theta = P.add_variable('theta', size=k, vtype='continuous', lower=-10, upper=10)
theta

P.add_constraint(max(abs(M*theta - b)) <= 5)
P.minimize(theta)

(Here b is some vector treated as cvxopt matrix.) However, the error I get is the following:

TypeError                                 Traceback (most recent call last)
<ipython-input-11-8884e5cb14dc> in <module>
      3 theta
      4 
----> 5 P.add_constraint(max(abs(M*theta - b.T)) < 45)
      6 P.minimize(theta)
      7 

TypeError: 'Norm' object is not iterable

I was wondering if there is an alternative way of making these computations that would be acceptable to cvxopt?

回答1:

(Never really used this lib apart from smaller experiments years ago)

This looks like the culprit is the classic case of hidden-magic in those highly-complex automatic-transformation modelling system tools.

picos overloads abs in abs(M*theta - b)
- see: doc
- this results in type Norm (a picos-based type)
picos probably does not overload max in max(abs(M*theta - b.T))
- python's max-operator (not something customized from picos!) will be used which is based on linear-search on some iterable
- the iterable here would be the Norm object; but it's not iterable as the error shows