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The steepest descent dynamical system with control. Applications to constrained minimization

Alexandre Cabot (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Let H be a real Hilbert space, Φ 1 : H a convex function of class 𝒞 1 that we wish to minimize under the convex constraint S . A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [5]) applied to the non-smooth function Φ 1 + δ S . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function Φ 0 : H whose critical points coincide with S and a control...

The steepest descent dynamical system with control. Applications to constrained minimization

Alexandre Cabot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Let H be a real Hilbert space, Φ 1 : H a convex function of class 𝒞 1 that we wish to minimize under the convex constraint S. A classical approach consists in following the trajectories of the generalized steepest descent system (cf.   Brézis [CITE]) applied to the non-smooth function  Φ 1 + δ S . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function  Φ 0 : H whose critical points coincide with S and...

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