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Set-Valued and Variational Analysis

, Volume 24, Issue 4, pp 685–705 | Cite as

Legendre Transform and Applications to Finite and Infinite Optimization

  • Cristopher Hermosilla
Article

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.

Keywords

Convex functions of Legendre type Legendre transform Geodesic search methods Optimal control Convex state constraints Riemannian metrics 

Mathematics Subject Classification (2010)

MSC 65K05 MSC 90C51 MSC 93C15 MSC 49L25 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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