Implicit parametrizations and applications in optimization and control

Tiba Dan

doi:10.3934/mcrf.2020006

Article Contents

2020, Volume 10, Issue 3: 455-470. Doi: 10.3934/mcrf.2020006

This issue Previous Article Next Article Sparse optimal control for the heat equation with mixed control-state constraints

Implicit parametrizations and applications in optimization and control

Tiba Dan^1,2,

1.
Institute of Mathematics, Romanian Academy, P.O. BOX 1-764, 014700 Bucharest, Romania
2.
Academy of Romanian Scientists, Splaiul Independenţei 54, 050094 Bucharest, Romania

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

Received: February 2018

Revised: July 2018

Early access: December 2019

Published: July 2020

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Abstract

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.

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

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Figure 1. The admissible set in Ex.2

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Figure 2. The geometry in Ex.2

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Figure 3. Admissible set of points

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Figure 4. Optimal trajectory

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