Convex Optimization

What it is about

You learn the fundamentals and methods of convex optimization: analysis of convex sets and functions, optimality conditions, duality, and algorithms such as Simplex, gradient/Newton methods, and interior-point methods. In the end you will be able to formulate problems as convex optimization tasks, derive optimality and duality conditions, and apply appropriate solution methods.

What you will be able to do

• Characterize convex sets and convex functions
• Derive and apply Fritz-John- and KKT-optimality conditions
• Discuss qualification conditions for constraints
• Apply weak and strong duality as well as saddle-point theorem
• Formulate primal and dual problems and perform primal reconstruction
• Derive and apply gradient and subgradient methods
• Use Cutting-Plane methods to linearize convex problems
• Apply Simplex, gradient methods, Newton algorithms and basis-interior-point methods
• Consider step-size rules (e.g., Armijo-Goldstein)

What the module consists of

• LecturesConveying the theoretical foundations in instructor-centered form
• Exercises/TutorialsDeepening and applying the material in student-centered exercises

Teaching method

• LectureExplaining the theory during the lectures
• Exercises and tutorialsReview and consolidation of knowledge in exercises