Rima Manual: Nonlinear Problems

[ Contents | Previous: Cases | Next: Differentiation ]

Rima can be used to formulate nonlinear problems just like nonlinear problems, and will use ipopt to solve them if it's available.

rima.define"x, X"
nonlinear = rima.mp.new{
  sense = "minimise",
  objective = X[1]*X[4]*(X[1] + X[2] + X[3]) + X[3],
  c1 = rima.mp.C(rima.product{x=X}(x), ">=", 25),
  c2 = rima.mp.C(rima.sum{x=X}(x^2), "==", 40),
  X = { rima.free(1, 5), rima.free(1, 5), rima.free(1, 5), rima.free(1, 5) }
}

(This example is taken from the ipopt documentation. As usual, you can print the model:

print(nonlinear)
--> Minimise:
-->   X[1]*(X[1] + X[2] + X[3])*X[4] + X[3]
--> Subject to:
-->   c1: X[1]*X[2]*X[3]*X[4] >= 25
-->   c2: X[1]^2 + X[2]^2 + X[3]^2 + X[4]^2 == 40

rima.mp.solve will inspect the problem, work out that it's nonlinear and use ipopt. Keep in mind that when you solve, you don't get duals:

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Common Public License (CPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

NOTE: You are using Ipopt by default with the MUMPS linear solver.
      Other linear solvers might be more efficient (see Ipopt documentation).


primal = rima.mp.solve(nonlinear)
print(primal.objective)                           --> 17.014

[ Contents | Previous: Cases | Next: Differentiation ]