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Journal Articles Set-Valued and Variational Analysis Year : 2016

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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Dates and versions

hal-01055917 , version 1 (14-08-2014)
hal-01055917 , version 2 (14-04-2016)

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Cristopher Hermosilla. Legendre Transform and Applications to Finite and Infinite Optimization. Set-Valued and Variational Analysis, 2016, ⟨10.1007/s11228-016-0368-5⟩. ⟨hal-01055917v2⟩
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