PICOS: A Python interface to conic optimization solvers#

PICOS logo

PICOS is a Python API that offers a convenient interface to various conic and integer programming solvers. Through PICOS, users can define optimization problems using high-level models, which support intricate vector, matrix variables, and multidimensional algebra. Once the problem is defined, PICOS automatically converts it into a format that’s comprehensible by any suitable solver present during runtime. This flexibility ensures that applications remain adaptable, giving users the liberty to select from multiple commercial or open-source solvers.

As with CVXPY, CORNETO allows to use PICOS as a backend for solving optimization problems. While CVXPY and PICOS have similar philosophy, their specific features, functions, and supported solvers might differ. Users might opt for one over the other based on individual needs or preferences.

CORNETO can be seen also as a multi-backend implementation of PICOS and CVXPY. You can choose the backend you prefer, and CORNETO will take care of the rest.

import corneto as cn

cn.info()
Installed version:v1.0.0a0 (latest: v1.0.0-alpha)
Available backends:CVXPY v1.5.3, PICOS v2.4.17
Default backend (corneto.opt):CVXPY
Installed solvers:CLARABEL, CVXOPT, ECOS, ECOS_BB, GLPK, GLPK_MI, OSQP, SCIP, SCIPY, SCS
Graphviz version:v0.20.3
Repository:https://github.com/saezlab/corneto
 
import numpy as np

from corneto.backend import PicosBackend

backend = PicosBackend()
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
# Convex optimization problem
P.add_objectives(sum(A @ x - b))
picos_model = P.solve(solver="cvxopt", verbosity=1)

===================================
           PICOS 2.4.17            
===================================
Problem type: Linear Program.
Searching a solution strategy for CVXOPT.
Solution strategy:
  1. ExtraOptions
  2. CVXOPTSolver
Applying ExtraOptions.
Building a CVXOPT problem instance.
Starting solution search.
-----------------------------------
 Python Convex Optimization Solver 
    via internal CONELP solver     
-----------------------------------
     pcost       dcost       gap    pres   dres   k/t
 0:  1.3020e+00  1.3020e+00  2e+00  2e-16  1e+00  1e+00
 1:  1.1568e+00  1.1401e+00  5e-01  1e-16  3e-01  3e-01
 2:  7.4020e-01  7.0348e-01  1e-01  3e-16  8e-02  3e-02
 3:  7.0098e-01  7.0046e-01  2e-03  1e-16  1e-03  4e-04
 4:  7.0001e-01  7.0000e-01  2e-05  2e-16  1e-05  4e-06
 5:  7.0000e-01  7.0000e-01  2e-07  1e-16  1e-07  4e-08
 6:  7.0000e-01  7.0000e-01  2e-09  1e-16  1e-09  4e-10
Optimal solution found.
------------[ CVXOPT ]-------------
Solver claims optimal solution for feasible problem.
Applying the solution.
Applied solution is primal feasible.
Search 1.4e-02s, solve 1.8e-02s, overhead 31%.
=============[ PICOS ]=============

P.symbols

{'x': <5×1 Real Variable: x>}

sum(P.symbols["x"].value)

1.0000000000000002

type(P)

corneto.backend._base.ProblemDef

P.objectives

[<1×1 Real Affine Expression: ([2×5]·x - [2×1])[0] + ([2×5]·x - [2×1])[1]>]

P.objectives[0].value

-0.29999999901748486

type(picos_model)

picos.modeling.problem.Problem

picos_model.value

-0.29999999901748486

type(A @ x)

corneto.backend._picos_backend.PicosExpression

type((A @ x).e)

picos.expressions.exp_affine.AffineExpression
Show Source