Towards Data Science is a community-powered publication that showcases work in data science, machine learning and artificial intelligence. Every day newcomers, seasoned researchers and industry practitioners publish tutorials, research notes and real-world case studies that help the field move forward.

Towards Data Science

A walkthrough of how to solve separable nonlinear constrained optimization problems by approximating nonlinear terms with piecewise linear (PWL) functions and solving the result with LP/MIP solvers. Covers separable program formulation, convex combination parametrization, Special Ordered Sets of Type 2 (SOS2) constraints for enforcing adjacency, and the theoretical relationship between convexity/concavity and approximation quality. Includes a portfolio selection example implemented in Python using Gurobipy, with results showing how increasing breakpoints improves solution accuracy.

A Gentle Introduction to Nonlinear Constrained Optimization with Piecewise Linear Approximations