This article explains how to transform separable nonlinear programming models into piecewise‑linear (PWL) approximations, use SOS‑type 2 constraints, and implement the whole workflow in Python with Gurobi, illustrating the method with a portfolio‑selection example and showing how breakpoint refinement improves solution accuracy.
This article presents the challenges faced by Chinese oil‑and‑chemical enterprises in the dual‑carbon era, introduces a comprehensive production‑planning optimization model and an integrated upstream‑downstream oil‑chain model, details large‑scale non‑convex nonlinear problem solving algorithms, and demonstrates numerous practical applications such as crude‑oil selection, carbon‑footprint tracking, and multi‑plant resource allocation.
This article introduces nonlinear programming, explains its challenges compared to linear programming, and demonstrates two concrete optimization examples solved with Python's SciPy library using gradient‑descent and SLSQP algorithms, complete with code and result interpretation.
