Legendre Transform and Applications to Finite and Infinite Optimization
march, 2016
Type de publication :
Article (revues avec comité de lecture)
Journal :
Set-Valued and Variational Analysis, vol. 24 (4), pp. 685–705
Editeur :
Springer
HAL :
Mots clés :
Mayer problem; Value Function; State constraints; Riemannian manifold; Riemannian metrics; Convex functions of Legendre type; Legendre transform coordinates; geodesic search methods; Optimal control of differential inclusions;
Résumé :
We investigate convex constrained nonlinear optimization problems and optimal control with convex state constraints in the light of the so-called Legendre transform. We use this change of coordinate to propose a gradient-like algorithm for mathematical programs, which can be seen as a search method along geodesics. We also use the Legendre transform to study the value function of a state constrained Mayer problem and we show that it can be characterized as the unique viscosity solution of the Hamilton-Jacobi-Bellman equation.
BibTeX :
@article{Her-2016,
author={Cristopher Hermosilla },
title={Legendre Transform and Applications to Finite and Infinite
Optimization },
doi={10.1007/s11228-016-0368-5 },
journal={Set-Valued and Variational Analysis },
year={2016 },
month={3},
volume={24 (4) },
pages={685–705},
}