Legendre Transform and Applications to Finite and Infinite Optimization

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.

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Correspondence to Cristopher Hermosilla.

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Hermosilla, C. Legendre Transform and Applications to Finite and Infinite Optimization. Set-Valued Var. Anal 24, 685–705 (2016). https://doi.org/10.1007/s11228-016-0368-5

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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