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Implicit parametrizations and applications in optimization and control

Dedicated to Prof. Dr. Fréderic Bonnans on the occasion of his 60th birthday

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  • We discuss necessary conditions (with less Lagrange multipliers), perturbations and general algorithms in non convex optimization problems. Optimal control problems with mixed constraints, governed by ordinary differential equations, are also studied in this context. Our treatment is based on a recent approach to implicit systems, constructing parametrizations of the corresponding manifold, via iterated Hamiltonian equations.

    Mathematics Subject Classification: Primary: 26B10, 34A12, 49K21; Secondary: 49M37, 36H05.


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  • Figure 1.  The admissible set in Ex.2

    Figure 2.  The geometry in Ex.2

    Figure 3.  Admissible set of points

    Figure 4.  Optimal trajectory

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