Optimization in Bifurcation Problems using a Continuation Method
J. P. Kernévez, Eusebius J. Doedel · Birkhäuser Basel eBooks · 1987
This paper deals with equations where u denotes a state variable , λ a control variable , and to which we want to find solution pairs (λ 0 , u 0 ) that maximize an objective functional g (λ, u ). Our specific objectives are (i) optimization in systems that have bifurcations, and (ii) control of the bifurcation phenomena themselves. Above g : ∆× U → R and f : ∆× U are continuously Fréchet differentiable mappings with ∆, U , and Y real Banach spaces. In particular ∆ may be R m . Let X ≡ ∆× U , with element x =(λ, u ). We state a general result on the validity of an optimality system and we give a continuation algorithm for finding optimal solutions. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.