Minimization of Energy Functionals Applied to Some Inverse Problems

Minimization of Energy Functionals Applied to Some Inverse Problems We consider a general class of problems of the minimization of convex integral functionals subject to linear constraints. Using Fenchel duality, we prove the equality of the values of the minimization problem and its associated dual problem. This equality is a variational criterion for the existence of a solution to a large class of inverse problems entering the class of generalized Fredholm integral equations. In particular, our abstract results are applied to marginal problems for stochastic processes. Such problems naturally arise from the probabilistic approaches to quantum mechanics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Minimization of Energy Functionals Applied to Some Inverse Problems

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 2001 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-001-0019-5
Publisher site
See Article on Publisher Site

Abstract

We consider a general class of problems of the minimization of convex integral functionals subject to linear constraints. Using Fenchel duality, we prove the equality of the values of the minimization problem and its associated dual problem. This equality is a variational criterion for the existence of a solution to a large class of inverse problems entering the class of generalized Fredholm integral equations. In particular, our abstract results are applied to marginal problems for stochastic processes. Such problems naturally arise from the probabilistic approaches to quantum mechanics.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2001

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