Minimization of Energy Functionals Applied to Some Inverse Problems
Minimization of Energy Functionals Applied to Some Inverse Problems
复制标题
应用于某些反问题的能量泛函最小化
DOI：
10.1007/s00245-001-0019-5
复制
发表时间：
2001
影响因子：
1.8
通讯作者：
C. Léonard
中科院分区：
文献类型：
--
作者：
C. Léonard
抽象。我们考虑一类一般的线性约束下凸积分泛函的极小化问题。利用Fenchel对偶，我们证明了极小化问题和它的对偶问题的值相等。这个等式是一个变分准则的一个大类的反问题进入类广义Fredholm积分方程的解决方案的存在。特别是，我们的抽象结果适用于随机过程的边际问题。这样的问题自然产生于量子力学的概率方法。
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.