A convex analysis approach to hybrid binary-continuous optimal control problems

Add to your list(s) Download to your calendar using vCal

• Christian Clason (University Duisburg-Essen)
• Monday 28 April 2014, 15:00-16:00
• MR 14, CMS.

If you have a question about this talk, please contact Carola-Bibiane Schoenlieb.

This talk is concerned with infinite-dimensional optimization problems where a distributed function should only take on values from a set of allowed states. This property can be promoted with the aid of a L⁰-type penalty that is zero on the admissible set and one otherwise. Possible applications include sparse, integer (“multi-bang”) and switching control. Although functionals involving such binary terms are non-convex and lack weak lower-semicontinuity, application of Fenchel duality yields a formal primal-dual optimality system that admits a unique solution. This solution is in general only suboptimal, but the optimality gap can be characterized and shown to be zero under appropriate conditions. A regularized semismooth Newton method allows the numerical computation of (sub)optimal solutions. For the case of multi-bang controls, in certain situations it is possible to derive a generalized multi-bang principle, i. e., to prove that the control almost everywhere takes on allowed values except possibly on a singular set. Numerical examples illustrate the effectiveness of the proposed approach.

This talk is part of the Applied and Computational Analysis series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• Applied and Computational Analysis
• CMS Events
• DAMTP info aggregator
• Featured lists
• Interested Talks
• MR 14, CMS
• My seminars
• Type the title of a new list here
• bld31

Note that ex-directory lists are not shown.