python-optimization

Library selection depends on problem type and scale. Scipy handles unconstrained and simple constrained problems efficiently. Cvxpy suits convex optimization with elegant syntax. Pyomo scales to large mixed-integer and complex problems. GEKKO excels at nonlinear and dynamic optimization. Match your problem classification—LP, QP, NLP, MIP, or global—to the library's strengths.

Linear programming (LP) minimizes a linear objective subject to linear constraints, solved rapidly with simplex methods. Quadratic programming (QP) adds squared terms to the objective or constraints, requiring specialized QP solvers. Nonlinear programming (NLP) includes arbitrary nonlinear functions; it's harder to solve and may have multiple local optima. Classification determines which solver to use.

Define your objective function, decision variables, and constraints; classify the problem type (LP, QP, NLP, MIP, convex, or global). Select the appropriate library and solver. Implement using end-to-end patterns: initialize variables, add constraints, configure the solver, and extract results. Robust patterns handle numerical stability and convergence issues.

Yes, both pyomo and cvxpy support mixed-integer programming (MIP). Pyomo integrates with industrial solvers like CPLEX and Gurobi for production-scale problems. Cvxpy works with open-source MIP solvers. MIP adds discrete decision variables to LP or NLP formulations, enabling applications in scheduling, routing, and resource allocation.

Convex optimization guarantees that any local minimum is a global minimum, enabling efficient, reliable solutions. It applies to portfolio optimization, resource allocation, and machine learning loss minimization. Cvxpy and GEKKO detect convexity automatically. Non-convex problems may require global optimization techniques or local solvers with multiple starting points.

Use global optimization when the problem is non-convex and local optima could be far from the global minimum, or when you need the best possible solution regardless of computation time. Global methods explore the entire search space. GEKKO and scipy support global optimization. Trade computation time against solution quality based on your problem's constraints.