Legendre Transform and Applications to Finite and Infinite Optimization

Cristopher Hermosilla 1, 2
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
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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https://hal.inria.fr/hal-01055917
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Submitted on : Thursday, April 14, 2016 - 5:26:58 PM
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Cristopher Hermosilla. Legendre Transform and Applications to Finite and Infinite Optimization. Set-Valued and Variational Analysis, Springer, 2016, ⟨10.1007/s11228-016-0368-5⟩. ⟨hal-01055917v2⟩

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