Power System State Estimation and Bad Data Detection by Means of Conic Relaxation

This paper is concerned with the power system state estimation problem, which aims to find the unknown operating point of a power network based on a set of available measurements. We design a penalized semidefinite programming (SDP) relaxation whose objective function consists of a surrogate for rank and an l1-norm penalty accounting for noise. Although the proposed method does not rely on initialization, its performance can be improved in presence of an initial guess for the solution. First, a sufficient condition is derived with respect to the closeness of the initial guess to the true solution to guarantee the success of the penalized SDP relaxation in the noiseless case. Second, we show that a limited number of incorrect measurements with arbitrary values have no effect on the recovery of the true solution. Furthermore, we develop a bound for the accuracy of the estimation in the case where a limited number of measurements are corrupted with arbitrarily large values and the remaining measurements are perturbed with modest noise values. The proposed technique is demonstrated on a large-scale 1354-bus European system

Conic Optimization Theory: Convexification Techniques and Numerical Algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.Comment: 18 page

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Robust computational intelligence techniques for visual information processing

The third part is exclusively dedicated to the super-resolution of Magnetic Resonance Images. In one of these works, an algorithm based on the random shifting technique is developed. Besides, we studied noise removal and resolution enhancement simultaneously. To end, the cost function of deep networks has been modified by different combinations of norms in order to improve their training. Finally, the general conclusions of the research are presented and discussed, as well as the possible future research lines that are able to make use of the results obtained in this Ph.D. thesis.This Ph.D. thesis is about image processing by computational intelligence techniques. Firstly, a general overview of this book is carried out, where the motivation, the hypothesis, the objectives, and the methodology employed are described. The use and analysis of different mathematical norms will be our goal. After that, state of the art focused on the applications of the image processing proposals is presented. In addition, the fundamentals of the image modalities, with particular attention to magnetic resonance, and the learning techniques used in this research, mainly based on neural networks, are summarized. To end up, the mathematical framework on which this work is based on, ₚ-norms, is defined. Three different parts associated with image processing techniques follow. The first non-introductory part of this book collects the developments which are about image segmentation. Two of them are applications for video surveillance tasks and try to model the background of a scenario using a specific camera. The other work is centered on the medical field, where the goal of segmenting diabetic wounds of a very heterogeneous dataset is addressed. The second part is focused on the optimization and implementation of new models for curve and surface fitting in two and three dimensions, respectively. The first work presents a parabola fitting algorithm based on the measurement of the distances of the interior and exterior points to the focus and the directrix. The second work changes to an ellipse shape, and it ensembles the information of multiple fitting methods. Last, the ellipsoid problem is addressed in a similar way to the parabola