CVXPY: Convex optimization, for everyone#
CVXPY is an open-source Python tool tailored for convex optimization problems. Unlike many platforms which require you to express your problem in strict formats determined by optimization solvers, CVXPY allows users to lay out their problem in a way that follows the maths.
A significant benefit of this is that CVXPY decouples the problem’s formulation from the solver used to tackle it. This means that once a problem is defined within CVXPY, one can seamlessly switch between or experiment with different solvers without the need to adjust the problem’s representation. Additionally, CVXPY supports an extensive range of both commercial and open-source solvers, providing users with the flexibility to choose the most appropriate tool for their specific challenges, be it for experimentation or scalability. This versatility simplifies the optimization process, making it more accessible and efficient.
import corneto as cn
cn.info()
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import numpy as np
from corneto.backend import CvxpyBackend
backend = CvxpyBackend()
P = backend.Problem()
A = np.array([[0.12, 0.92, 0.76, 0.98, 0.79], [0.58, 0.57, 0.53, 0.71, 0.55]])
b = np.array([1, 0])
x = backend.Variable("x", A.shape[1])
P += sum(x) == 1, x >= 0
P.add_objectives(sum(A @ x - b))
cvxpy_model = P.solve(verbosity=1)
===============================================================================
CVXPY
v1.6.5
===============================================================================
(CVXPY) Apr 17 03:24:11 PM: Your problem has 5 variables, 6 constraints, and 0 parameters.
(CVXPY) Apr 17 03:24:11 PM: It is compliant with the following grammars: DCP, DQCP
(CVXPY) Apr 17 03:24:11 PM: (If you need to solve this problem multiple times, but with different data, consider using parameters.)
(CVXPY) Apr 17 03:24:11 PM: CVXPY will first compile your problem; then, it will invoke a numerical solver to obtain a solution.
(CVXPY) Apr 17 03:24:11 PM: Your problem is compiled with the CPP canonicalization backend.
-------------------------------------------------------------------------------
Compilation
-------------------------------------------------------------------------------
(CVXPY) Apr 17 03:24:11 PM: Compiling problem (target solver=SCIP).
(CVXPY) Apr 17 03:24:11 PM: Reduction chain: Dcp2Cone -> CvxAttr2Constr -> ConeMatrixStuffing -> SCIP
(CVXPY) Apr 17 03:24:11 PM: Applying reduction Dcp2Cone
(CVXPY) Apr 17 03:24:11 PM: Applying reduction CvxAttr2Constr
(CVXPY) Apr 17 03:24:11 PM: Applying reduction ConeMatrixStuffing
(CVXPY) Apr 17 03:24:11 PM: Applying reduction SCIP
(CVXPY) Apr 17 03:24:11 PM: Finished problem compilation (took 1.048e-02 seconds).
-------------------------------------------------------------------------------
Numerical solver
-------------------------------------------------------------------------------
(CVXPY) Apr 17 03:24:11 PM: Invoking solver SCIP to obtain a solution.
presolving:
(0.0s) symmetry computation started: requiring (bin +, int +, cont +), (fixed: bin -, int -, cont -)
(0.0s) no symmetry present (symcode time: 0.00)
presolving (0 rounds: 0 fast, 0 medium, 0 exhaustive):
0 deleted vars, 0 deleted constraints, 0 added constraints, 0 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients
0 implications, 0 cliques
presolved problem has 5 variables (0 bin, 0 int, 0 impl, 5 cont) and 6 constraints
6 constraints of type <linear>
Presolving Time: 0.00
time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl.
* 0.0s| 1 | 0 | 1 | - | LP | 0 | 5 | 6 | 1 | 0 | 0 | 0 | 0 | 7.000000e-01 | 7.000000e-01 | 0.00%| unknown
0.0s| 1 | 0 | 1 | - | 608k | 0 | 5 | 6 | 1 | 0 | 0 | 0 | 0 | 7.000000e-01 | 7.000000e-01 | 0.00%| unknown
SCIP Status : problem is solved [optimal solution found]
Solving Time (sec) : 0.00
Solving Nodes : 1
Primal Bound : +7.00000000000000e-01 (1 solutions)
Dual Bound : +7.00000000000000e-01
Gap : 0.00 %
-------------------------------------------------------------------------------
Summary
-------------------------------------------------------------------------------
(CVXPY) Apr 17 03:24:11 PM: Problem status: optimal
(CVXPY) Apr 17 03:24:11 PM: Optimal value: -3.000e-01
(CVXPY) Apr 17 03:24:11 PM: Compilation took 1.048e-02 seconds
(CVXPY) Apr 17 03:24:11 PM: Solver (including time spent in interface) took 3.968e-03 seconds
P.objectives[0].value
np.float64(-0.30000000000000004)
type(P)
corneto.backend._base.ProblemDef
type(cvxpy_model)
cvxpy.problems.problem.Problem
cvxpy_model.status
'optimal'