NLP

Non-convex & Higher-order NLP

Degree-3+ polynomials, non-smooth penalties, dense or implicit Hessians.

In plain terms

Some problems have a “landscape” full of hills and valleys, where the best spot hides among many almost-as-good ones and the math turns steep and tangled. Classic methods need a detailed map (second derivatives) that is expensive or impossible to compute. Quicopt only needs to feel the slope under its feet.

The technical picture

Smooth and non-smooth non-linear problems where Newton-class methods stall — because the objective is higher-order and non-convex, or because the KKT factorization is dominated by a dense, sparse-but-filling, or implicit Hessian reachable only through a simulator or learned model.

Quicopt is purely first-order: it needs gradients only — no Hessian, no factorization — and it optimizes the original objective, without the auxiliary-variable reformulations or piecewise approximations that quietly change the problem.

Mathematical model▾

Minimize a higher-order, non-convex objective over continuous variables; constraints optional.

x \in R^{n} min s.t. f (x) g (x) \leq 0

with f, g non-linear, possibly non-convex; gradients only.

Example

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

Install the client

$ pip install "quicopt[pyomo]"

Copy the example

nlp.py

import pyomo.environ as pyo
from quicopt import Client

# An NLP: a smooth non-linear objective (exp, log) under a linear constraint.
m = pyo.ConcreteModel()
m.x = pyo.Var(bounds=(0.1, 10))
m.y = pyo.Var(bounds=(0.1, 10))
m.budget = pyo.Constraint(expr=m.x + m.y <= 8)
m.obj = pyo.Objective(expr=pyo.exp(-m.x) + pyo.log(m.y) + m.x**2, sense=pyo.minimize)

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

Run it

$ python nlp.py

What you’ll see

├── status:     optimal
├── feasible:   true
├── objective:  -1.4754011643639007
├── x:          x1=0.3517, x2=0.1  (2 variables)
└── solve_time: 0.0258 s

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

Benchmark

How Quicopt performs on representative non-convex, higher-order problems.

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.