Modules

Prerequisites

Contents

Unrestricted optimization Optimality criteria, sensitivity, line search methods (e.g. gradient methods, CG methods, Newton methods, Quasinewton methods) and trust region methods, as well as their globalisations Restricted optimization Karush-Kuhn-Tucker theory (first and second order constraints, regularity), sensitivity, penalty and barrier methods, augmented Lagrangian methods, Lagrangian-Newton methods, SQP methods, nonlinear interior point methods Studnets gain experience in independent scientific work by working out a project, and learn how to present and communicate mathematical results by presenting the results to the group. • Development of a project (independent scientific work) • Presentation of the results to the group (presentation and communication of mathematical results)

Learning outcomes

After successful completion of the module, students know the problem types of differentiable optimization as well as the theory and procedures of differentiable optimization. They can create and evaluate different formulations of a problem, as well as select and evaluate appropriate procedures. By working out a project, they have gained experience in independent scientific work. By presenting the results to the group, they have learned how to present and communicate mathematical results.

Assessment

Prerequisite: • Successful completion of a project Final module examination: • Oral examination, 30 min.

Remarks

• Study programme Artificial Intelligence M.Sc.: Compulsory elective modul in complex „Learning and Reasoning" • Study programme Mathematics M.Sc.: Compulsory elective modul in complex „Optimization"