问题
I am trying to recreate an integer linear optimization problem using cvxpy that I have outlined in Excel - . Note that this is a dummy example, the actual dataset will have thousands of variables. Please ignore the solution in cell K5 of the spreadsheet, as Excel Solver isn't able to provide integer solutions.
Consider that the 9 variables are split into 3 buckets. Note my goal with constraints 1-3 is that either there are at least 2 out of 3 1's for a bucket of variables, or all of the values are 0. For example, a,b,c should be either 1,1,1 or 1, 1, 0 or 1,0,1 or 0, 1, 1, or 0, 0, 0.
import numpy as np
import cvxpy as cp
import cvxopt
coefs= np.array([0.7, 0.95, 0.3, 2, 1.05, 2.2, 4, 1, 3])
dec_vars = cp.Variable(len(coefs), boolean = True)
constr1 = np.array([1,1,1,0,0,0,0,0,0]) @ dec_vars == 2 * max(dec_vars[0:3])
constr2 = np.array([0,0,0,1,1,1,0,0,0]) @ dec_vars == 2 * max(dec_vars[3:6])
constr3 = np.array([0,0,0,0,0,0,1,1,1]) @ dec_vars == 2 * max(dec_vars[6:9])
constr4 = np.ones(len(coefs)) @ dec_vars >= 2
When I run up to here, I get a
NotImplementedError: Strict inequalities are not allowed. error
回答1:
The core issue is your usage of python's max which is tried to be evaluated before reaching cvxpy. You cannot use just any python-native function on cvxpy-objects. max(cvx_vars) is not supported as is abs(cvx_vars) and much more.
There is max-function in cvxpy, namely: cp.max(...), but i don't get what you are trying to do or how you would achieve this by exploiting max. See below...
Note my goal with constraints 1-3 is that either there are at least 2 out of 3 1's for a bucket of variables, or all of the values are 0. For example, a,b,c should be either 1,1,1 or 1, 1, 0 or 1,0,1 or 0, 1, 1, or 0, 0, 0.
This, in general, needs some kind of disjunctive reasoning.
Approach A
The general approach would be using a binary indicator variable together with a big-M based expression:
is_zero = binary aux-var
sum(dec_vars) <= 3 * is_zero
sum(dec_vars) >= 2 * is_zero
Approach B
Alternatively, one could also model this by (without aux-vars):
a -> b || c
b -> a || c
c -> a || b
meaning: if there is a non-zero, there is at least one more non-zero needed. This would look like:
(1-a) + b + c >= 1
(1-b) + a + c >= 1
(1-c) + a + b >= 1
来源：https://stackoverflow.com/questions/65416823/specifying-complex-constraints-in-cvxpy-yields-strict-inequalities-error