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SUMMARY:A convex analysis approach to hybrid binary-continuous optimal con
 trol problems - Christian Clason (University Duisburg-Essen)
DTSTART:20140428T140000Z
DTEND:20140428T150000Z
UID:TALK51768@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:This talk is concerned with infinite-dimensional optimization 
 problems where a distributed function should only take on values from a se
 t of allowed states. This property can be promoted with the aid of a L<sup
 >0</sup>-type penalty that is zero on the admissible set and one otherwise
 . Possible applications include sparse\, integer ("multi-bang") and switch
 ing control. Although functionals involving such binary terms are non-conv
 ex and lack weak lower-semicontinuity\, application of Fenchel duality yie
 lds a formal primal-dual optimality system that admits a unique solution. 
 This solution is in general only suboptimal\, but the optimality gap can b
 e characterized and shown to be zero under appropriate conditions. A regul
 arized semismooth Newton method allows the numerical computation of (sub)o
 ptimal solutions. For the case of multi-bang controls\, in certain situati
 ons 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 effectivene
 ss of the proposed approach.
LOCATION:MR 14\, CMS
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