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Legendre Transform and Applications to Finite and Infinite Optimization

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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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  1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803–4918, USA

    Cristopher Hermosilla

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  1. 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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