Legendre Transform and Applications to Finite and Infinite Optimization

Cristopher Hermosilla

march, 2016

Publication type:

Paper in peer-reviewed journals

Journal:

Set-Valued and Variational Analysis, vol. 24 (4), pp. 685–705

Publisher:

Springer

DOI:

10.1007/s11228-016-0368-5

HAL:

hal-01055917

Keywords :

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;

Abstract:

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},
}