Variational Networks: An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration

Variational Methods in Image Restoration 1

Optimal Control Methods and the Variational Approach to Differential Equations

The calculus of variations is an important tool in the study of boundary value problems for differential systems. A development of this approach, called the control variational method, is based on the use of the optimal control theory, especially of the Pontryagin maximum principle. In this presentation, we review the results established in the literature on the control variational method and i...

VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

Variational Iteration Method for Image Restoration

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called the Variational Iteration Method (VIM) and the correspondent approximated solutions will be obtained for the P-M equation with regards to relevant error analysis. Thr...

Optimal stopping with dynamic variational preferences

We consider optimal stopping problems in uncertain environments for an agent assessing utility by virtue of dynamic variational preferences as in [15] or, equivalently, assessing risk by dynamic convex risk measures as in [4]. The solution is achieved by generalizing the approach in [20] introducing the concept of variational supermartingales and an accompanying theory. To illustrate results, w...