Solve a polynomial optimization problem
Create a random polynomial of degree k using the Dot operator and find its minimum using the Nonlinear solver.
Further explanation of this example: 'Xpress Python Reference Manual'
#!/bin/env python # # Minimize a polynomial constructed with the Dot product # from __future__ import print_function import xpress as xp import numpy as np # # Generate a random coefficient tensor T of dimension k + 1 and sizes # n+1 for each dimension except for the first, which is h, then use it # to create h polynomial constraints. The lhs of each constraint has a # polynomial of degree k, and not homogeneous as we amend the vector # of variable with the constant 1. This is accomplished via a single # dot product. # n = 10 # dimension of variable space h = 3 # number of polynomial constraints k = 4 # degree of each polynomial # Vector of n variables x = np.array( + [xp.var(lb=-10, ub=10) for _ in range(n-1)]) sizes = [n]*k # creates list [n,n,...,n] of k elements # Operator * before a list translates the list into its # (unparenthesized) tuple, i.e., the result is a reshape list of # argument that looks like (h, n, n, ..., n) T = np.random.random(h * n ** k).reshape(h, *sizes) print(T) T2list = [x]*k compact = xp.Dot(T, *T2list) <= 0 p = xp.problem() p.addVariable(x[1:]) p.addConstraint(compact) p.write('polynomial', 'lp')
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