7. Constrained Nonlinear Optimization

Learning Objectives

1. Explain neccessary and sufficient optimality conditions, analyze candidate solutions

2. Implement basic algorithms including Newton’s method, trust regions, line searches in Python

3. Prove basic properties of algorithms such as local convergence rates

Sections

• 7.1. Convexity Revisited
• 7.2. Local Optimality Conditions
• 7.3. Analysis of KKT Conditions
• 7.4. Constraint Qualifications
• 7.5. Second Order Optimality Conditions
• 7.6. NLP Diagnostics with Degeneracy Hunter
• 7.7. Simple Netwon Method for Equality Constrained NLPs
• 7.8. Inertia-Corrected Netwon Method for Equality Constrained NLPs