We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the solution map is studied. Directional differentiability is proved both for finite-dimensional and function space problems, under suitable assumptions on the ac...

The Topological Active Net (TAN) model is a deformable model used for image segmentation. It integrates features of region–based and edge–based segmentation techniques. This way, the model is able to fit the edges of the objects and model their inner topology. The model consists of a two dimensional mesh controlled by energy functions. The minimization of these energy functions leads to the TAN...

We consider partially-specified optimization problems where the goal is to actively, but efficiently, acquire missing information about the problem in order to solve it. An algorithm designer wishes to solve a linear program (LP), max cx s.t. Ax ≤ b,x ≥ 0, but does not initially know some of the parameters. The algorithm can iteratively choose an unknown parameter and gather information in the ...

This paper addresses the numerical approximation of Young measures appearing as generalized solutions to scalar nonconvex variational problems. We prove a priori and a posteriori error estimates for a macroscopic quantity, the stress. For a scalar three-well problem we show convergence of other quantities such as Young measure support and microstructure region. Numerical experiments indicate th...

Convex Transductive Experimental Design (CTED) is one of the most representative active learning methods. It utilizes a data reconstruction framework to select informative samples for manual annotation. However, we observe that CTED cannot well handle the diversity of selected samples and hence the set of selected samples may contain mutually similar samples which convey similar or overlapped i...