A nonsmooth optimization approach to sensor network localization

In this paper the problem of localization of wireless sensor network is formulated as an unconstrained nonsmooth optimization problem. We minimize a distance objective function which incorporates unknown sensor nodes and nodes with known positions (anchors) in contrast to popular semidefinite programming (SDP) methods which use artificial objective functions. We study the main properties of the objective function in this problem and design an algorithm for its minimization. Our algorithm is a derivative-free discrete gradient method that allows one to find a near global solution. The algorithm can handle a large number of sensors in the network. This paper contains the theory of our proposed formulation and algorithm while experimental results are included in later work

New optimization methods in Data Mining

Data mining is a modern area of science dealing with the learning from given data in order to make predictions and estimations. Applications of Data mining can be found in various areas of academical and non academical life. This paper introduces new contributions by continuous optimization as a key technology in data mining. The methods suggested for solution of such important problems as clustering and classification, were recently obtained by the authors in collaboration with members of EURO working group EUROPT

Application of nonsmooth optimisation to data analysis

The research presented in this thesis is two-fold: on the one hand, major data mining problems are reformulated as mathematical programming problems. These problems should be carefully designed, since from their formulation depends the efficiency, perhaps the existence, of the solvers. On the other hand, optimisation methods are adapted to solve these problems, most of which are nonsmooth and nonconvex. This part is delicate, as the solution is often required to be good and obtained fast. Numerical experiments on real-world datasets are presented and analysed.Doctor of Philosoph

Estimation of a regression function by maxima of minima of linear functions

In this paper, estimation of a regression function from independent and identically distributed random variables is considered. Estimates are defined by minimization of the empirical L2 risk over a class of functions, which are defined as maxima of minima of linear functions. Results concerning the rate of convergence of the estimates are derived. In particular, it is shown that for smooth regression functions satisfying the assumption of single index models, the estimate is able to achieve (up to some logarithmic factor) the corresponding optimal one-dimensional rate of convergence. Hence, under these assumptions, the estimate is able to circumvent the so-called curse of dimensionality. The small sample behavior of the estimates is illustrated by applying them to simulated data. © 2009 IEEE

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

A generic interior-point framework for nonsmooth and complementarity constrained nonlinear optimization

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