Tatiana Tchemisova

Spinning rough disc moving in a rarefied medium

We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from non-elastic interaction of gas particles with the body. We propose another (complementary) mechanism of creating the transversal force owing to multiple collisions of particles in cavities of the body surface. We limit ourselves to the two-dimensional case of a rough disc moving through a zero-temperature medium on the plane, where reflections of the particles from the body are elastic and mutual interaction of the particles is neglected. We represent the force acting on the disc and the moment of this force as functionals depending on ‘shape of the roughness’, and determine the set of all admissible forces. The disc trajectory is determined for several simple cases. The study is made by means of billiard theory, Monge–Kantorovich optimal mass transport and by numerical methods.

Force acting on a rough disk spinning in a flow of noninteracting particles

1. Consider a flow of point particles impinging on a body spinning around a fixed point. The particles do not interact with one another, and their collisions with the body are elastic. The goal is to determine the pressure force exerted by the flow on the body. The problem is considered in two dimensions. In the Euclidean space 2 , we introduce an orthonormal frame of reference Ox 1 x 2 . The flux density ρ is a constant. Initially, the particles move at the identical veloc-

Sufficient optimality conditions for convex semi-infinite programming

We consider a convex semi-infinite programming (SIP) problem whose objective and constraint functions are convex w.r.t. a finite-dimensional variable x and whose constraint function also depends on a so-called index variable that ranges over a compact set in . In our previous paper [O.I. Kostyukova, T.V. Tchemisova, and S.A. Yermalinskaya, On the algorithm of determination of immobile indices for convex SIP problems, IJAMAS Int. J. Math. Stat. 13(J08) (2008), pp. 13–33], we have proved an implicit optimality criterion that is based on concepts of immobile index and immobility order. This criterion permitted us to replace the optimality conditions for a feasible solution x 0 in the convex SIP problem by similar conditions for x 0 in certain finite nonlinear programming problems under the assumption that the active index set is finite in the original semi-infinite problem. In the present paper, we generalize the implicit optimality criterion for the case of an infinite active index set and obtain new first- and second-order sufficient optimality conditions for convex semi-infinite problems. The comparison with some other known optimality conditions is provided.

New Optimization Methods in Data Mining

Generally speaking, an optimization problem consists in maximization or minimization of some function (objective function) f : S → R. The feasible set S ⊆ Rn can be either finite or infinite, and can be described with the help of a finite or infinite number of equalities and inequalities or in the form of some topological structure in Rn. The methods for solution of a certain optimization problem depend mainly on the properties of the objective function and the feasible set. In this paper, we discuss how specific optimization methods of optimization can be used in some specific areas of data mining, namely, in classification and clustering that are considered interrelated [11]

On a constructive approach to optimality conditions for convex SIP problems with polyhedral index sets

In the paper, we consider a problem of convex Semi-Infinite Programming with an infinite index set in the form of a convex polyhedron. In study of this problem, we apply the approach suggested in our recent paper [Kostyukova OI, Tchemisova TV. Sufficient optimality conditions for convex Semi Infinite Programming. Optim. Methods Softw. 2010;25:279–297], and based on the notions of immobile indices and their immobility orders. The main result of the paper consists in explicit optimality conditions that do not use constraint qualifications and have the form of criterion. The comparison of the new optimality conditions with other known results is provided.

Modelling the problem of food distribution by the Portuguese food banks

A food bank is a non-profit, social solidarity organisation that typically distributes the donated food among a wide variety of local non-profit, social solidarity institutions which in turn feed the low-income people. The problem presented by the Portuguese Federation of Food Banks is to determine, for a specific food bank, the quantities of the donated products that must be assigned to each local social solidarity institution in order to satisfy the needs of the supported people as much as possible, without favouring any institution. We propose a linear programming model followed by a rounding heuristic to obtain a solution to the problem described. Computational results are reported.

Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets

In the present paper, we analyze a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and their immobility orders. Our previous work showcasing this approach includes a number of papers dealing with simpler cases of semi-infinite problems than the ones under consideration here. Key findings of the paper include the formulation and the proof of implicit and explicit optimality conditions under assumptions, which are less restrictive than the constraint qualifications traditionally used. In this perspective, the optimality conditions in question are also compared to those provided in the relevant literature. Finally, the way to formulate the obtained optimality conditions is demonstrated by applying the results of the paper to some special cases of the convex semi-infinite problems.

A Generator of Nonregular Semidefinite Programming Problems

Regularity is an important property of optimization problems. Various notions of regularity are known from the literature, being defined for different classes of problems. Usually, optimization methods are based on the optimality conditions, that in turn, often suppose that the problem is regular. Absence of regularity leads to theoretical and numerical difficulties, and solvers may fail to provide a trustworthy result. Therefore, it is very important to verify if a given problem is regular in terms of certain regularity conditions and in the case of nonregularity, to apply specific methods. On the other hand, in order to test new stopping criteria and the computational behaviour of new methods, it is important to have an access to sets of reasonably-sized nonregular test problems. The paper presents a generator that constructs nonregular Semidefinite Programming (SDP) instances with prescribed irregularity degrees and a database of nonregular test problems created using this generator. Numerical experiments using popular SDP solvers on the problems of the database are carried out and permit to conclude that the most popular SDP solvers are not efficient when applied to nonregular problems.

Special issue: optimization in the natural sciences

This volume of Optimization contains selected papers presented during the EURO Mini-Conference (MEC) on Optimization in the natural sciences, hosted by the University of Aveiro, Portugal, from 5–9 February 2014. The conference was the 30th event in the series initiated by EURO, Association of European OR Societies. The project of organizing MEC XXX was designed by EUROPT, EURO Working Group on Continuous Optimization (http://europt.iam.metu.edu.tr/), and supported by EURO (http://www.euro-online.org/) and CIDMA – the Center for Research and Development in Mathematics and Applications of the Mathematics Department of the University of Aveiro (cidma.mat.ua.pt/). This led to the choice of the theme of the mini-conference – Optimization in the natural sciences – that in turn reflected three directions of research that are being developed in EUROPT and CIDMA: Dynamical Systems, Optimization and Statistics with special attention to their applications in the natural sciences and bioinformatics. The conference topics reflected the diversity of different lines of research in optimization and its application in the natural sciences, including applications of modelling and optimization in physics, biology, chemistry and medicine; biomedical engineering; design optimization; data visualization for optimal decisions; image processing; linear and nonlinear programming, infinite and semiinfinite optimization with applications; inverse problems; multi-criteria optimization with applications; optimal control applied to biological models; optimal mass transfer; optimization in bioinformatics and computational biology; shape optimization; solution of optimization problems using statistical methods; statistical and probabilistic modelling; and others. The conference was attended by about 100 registered participants representing 21 countries. The talks by the invited speakers Giuseppe Buttazzo (University of Pisa), Leonid Bunimovich (Georgia State University, Atlanta), Alexander Dudin (Belarusian State University), Michael Greenacre (University Pompeu Fabra, Barcelona), Gueorgui Smirnov (University of Minho, Portugal) and Sergei Tabachnikov (Pennsylvania State University), aroused lively interest among the participants. Two tutorial lectures were offered by Yaroslav D. Sergeyev from the University of Calabria. The participants discussed recent achievements in optimization theory, exchanged experiences in solving real-world problems, reported on the latest developments of appropriate models of optimization and their applications in the natural sciences. The XXX EURO Mini-Conference provided an excellent forum for researchers and practitioners in optimization to promote their recent advances to the wider scientific community and to identify new research challenges in theory, methods and applications.

Optimization in the Natural Sciences

This book constitutes the refereed proceedings of the 30th Euro Mini-Conference, EmC-ONS 2014, held in Aveiro, Portugal, in February 2014. The 13 revised full papers presented were carefully reviewed and selected from 70 submissions. The papers are organized in topical sections on dynamical systems; optimization and applications; modeling and statistical techniques for data analysis.