Convex Duality and Applications in Mass Transport and Calculus of Variations

What it is about

You will learn foundations of convex duality and how they are applied in variational problems and in the theory of optimal mass transport. In the end you will be able to understand Legendre/Fenchel duality, dual formulations of optimization problems and central results of mass transport theory as well as explain simple numerical procedures for it.

What you will be able to do

• Understand convex sets and convex functions
• Apply separation theorems
• Master Legendre- and Fenchel-Rockafellar duality
• Analyze variational problems: direct methods and relaxation
• Understand Kantorovich duality in mass transport
• Insight into dynamic formulations and Wasserstein gradient flows
• Knowledge of basic numerical procedures for optimal transport (e.g. Sinkhorn, auction)

What the module consists of

• LecturePresentation of content with examples and discussion; central teaching component

Teaching method

• TafelvorlesungContent is explained and illustrated with demonstrative examples
• DiscussionInteractive reflection on the topics and encouragement of independent literature work
• Student presentation optionOpportunity to read and present a paper (see examination option)