We present an Outlier Removal Clustering (ORC) algorithm that provides outlier detection and data clustering simultaneously. The method employs both clustering and outlier discovery to improve estimation of the centroids of the generative distribution. The proposed algorithm consists of two stages. The first stage consist of purely K-means process, while the second stage iteratively removes the vectors which are far from their cluster centroids. We provide experimental results on three different synthetic datasets and three map images which were corrupted by lossy compression. The results indicate that the proposed method has a lower error on datasets with overlapping clusters than the competing methods.

We discuss a linear-quadratic optimal control problem with pointwise control and state constraints. The state constraints are regularized by a Lavrentiev type regularization. The main results of the paper are estimates for the regularization error and the stability with respect to noisy data.

We focus on optimal control problems governed by partial differential equations. The presence of constraints on the state provides numerical and analytical difficulties. We treat these obstacles introducing a Lavrentiev regularization. The key issue is addressed to the analytical investigation of the convergence order of solutions based on certain source representation arguments. A virtual control approach is investigated for problems with additional control constraints. Numerical experiments are presented.

Elliptic optimal control problems, State constraints, Discrete approximations, Error estimates, Mixed control-state constraints,