Linear Programming

Continuous variables, a linear objective, linear constraints.

In plain terms

Imagine you want the best plan — the cheapest, fastest, or most profitable — in a world where everything scales in straight lines: twice the input, twice the effect. Linear programming finds that best plan for you, even with thousands of options and limits to respect.

The technical picture

Linear programming is the foundation of mathematical optimization: minimize a linear objective over continuous variables subject to linear equalities and inequalities.

Established solvers handle linear programs at very large scale, and Quicopt supports them through the same modeling interface — so the linear parts of your problem live alongside any non-linear or combinatorial structure, in one model.

Mathematical model▾

Minimize a linear objective subject to linear constraints over non-negative continuous variables.

x \in R^{n} min s.t. c^{⊤} x A x \leq b x \geq 0

where c \in R^{n}, A \in R^{m \times n}, b \in R^{m} .

Example

From install to solved model — a small, self-contained example, copy-paste ready.

Install the client

$ pip install "quicopt[mathopt]"

Copy the example

lp.py

from ortools.math_opt.python import mathopt
from quicopt import Client

# A linear program: continuous variables, a linear objective, linear constraints.
model = mathopt.Model(name="lp")
x = model.add_variable(lb=0.0, name="x")
y = model.add_variable(lb=0.0, ub=6.0, name="y")
model.add_linear_constraint(x + 2 * y <= 14)
model.add_linear_constraint(3 * x - y >= 0)
model.maximize(3 * x + 4 * y)

client = Client("https://try.quicoptapi.pgi.fz-juelich.de")
result = client.solve(model)
print(result.display)

Run it

$ python lp.py

What you’ll see

├── status:     optimal
├── feasible:   true
├── objective:  42.0
├── x:          x=14, y=0  (2 variables)
└── solve_time: 0.0031 s

Docs, API reference and more examples live in the Developer Hub →

Benchmark

How Quicopt performs on representative linear programs.

Illustrative — pending measurement

QuicoptEstablished solver

Illustrative scaling — to be replaced with measured data.

Measured results for this class are being prepared and will appear here.