 SIGMAOPT SEMINAR
 Speaker: Dr C. Yalcin Kaya, University of South Australia
 Title: Numerical Methods For Convex Multiobjective Control Problems
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 2:00 pm, Wed, 9^{th} Jun 2010
 Abstract:
We consider multiobjective convex optimal control problems. First we state a relationship between the (weakly or properly) efficient set of the multiobjective problem and the solution of the problem scalarized via a convex combination of objectives through a vector of parameters (or weights). Then we establish that (i) the solution of the scalarized (parametric) problem for any given parameter vector is unique and (weakly or properly) efficient and (ii) for each solution in the (weakly or properly) efficient set, there exists at least one corresponding parameter vector for the scalarized problem yielding the same solution. Therefore the set of all parametric solutions (obtained by solving the scalarized problem) is equal to the efficient set. Next we consider an additional objective over the efficient set. Based on the main result, the new objective can instead be considered over the (parametric) solution set of the scalarized problem. For the purpose of constructing numerical methods, we point to existing solution differentiability results for parametric optimal control problems. We propose numerical methods and give an example application to illustrate our approach. This is joint work with Henri Bonnel (University of New Caledonia).
 Download: Seminar slides by C. Yalcin Kaya
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