# Tatiana TchemisovaUniversity of Aveiro | UA · Division of Mathematics

Tatiana Tchemisova

PhD

## About

50

Publications

3,747

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153

Citations

## Publications

Publications (50)

The paper is dedicated to the study of strong duality for a problem of linear copositive programming. Based on the recently introduced concept of the set of normalized immobile indices, an extended dual problem is deduced. The dual problem satisfies the strong duality relations and does not require any additional regularity assumptions such as cons...

The paper is devoted to the regularization of linear Copositive Programming problems which consists of transforming a problem to an equivalent form, where the Slater condition is satisfied and therefore the strong duality holds. We describe regularization algorithms based on a concept of immobile indices and on the understanding of the important ro...

Recently, for a linear copositive programming problem, we formulated an exact explicit dual problem in the form of the extended Lagrange-Slater dual. This dual problem is formulated using only the data of the primal copositive problem, satisfies the strong duality relation, and is obtained without any regularity assumptions due to the use of a conc...

In this paper, we continue an earlier study of the regularization procedures of linear copositive problems and present new algorithms that can be considered as modifications of the algorithm described in our previous publication, which is based on the concept of immobile indices. The main steps of the regularization algorithms proposed in this pape...

In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a...

The paper is devoted to the regularization of linear Copositive Programming problems which consists of transforming a problem to an equivalent form, where the Slater condition is satisfied and the strong duality holds. We describe here two regularization algorithms based on the concept of immobile indices and an understanding of the important role...

This manual aims to offer a supportive framework to all university staff members who endeavour to launch their students in the area of entrepreneurship and of starting up a business. We would like to
describe the former as “ABC”: Academic Business Coaches, as they are coming from and are still working in an academic environment while wanting to als...

More entrepreneurial life at European schools (MELES) project has been created as an
answer to an educational challenge, which is lack of effective tools that could be used to
increase social and professional activity of young generation entering the labor market
in order to make full use of their potential for the development of economy. This chal...

Regularisation consists in reducing a given optimisation problem to an equivalent form where certain regularity conditions, which guarantee the strong duality, are fulfilled. In this paper, for linear problems of semidefinite programming (SDP), we propose a regularisation procedure which is based on the concept of an immobile index set and its prop...

The paper is devoted to a study of the cone $\cop$ of copositive matrices. Based on the known from semi-infinite optimization concept of immobile indices, we define zero and minimal zero vectors of a subset of the cone $\cop$ and use them to obtain different representations of faces of $\cop$ and the corresponding dual cones. We describe the minima...

NOTE: The final version is labelled Aug_2020. This version corrects an error in the author names, and removes specific deadlines from the recommendations.
The WISDOM Forum was set up to provide a platform to support, empower and encourage the participation of all genders in Operational Research within EURO. 3 We cannot solve problems that we do no...

In this paper, we consider a special class of conic optimization problems, consisting of set-semidefinite(or K-semidefinite) programming problems, where the set K is a polyhedral convex cone. For these problems, we introduce the concept of immobile indices and study the properties of the set of normalized immobile indices and the feasible set. This...

The paper is dedicated to the study of strong duality for a problem of linear copositive programming. Based on the recently introduced concept of the set of normalized immobile indices, an extended dual problem is deduced. The dual problem satisfies the strong duality relations and does not require any additional regularity assumptions such as cons...

We consider problems of linear copositive programming where feasible sets consist of vectors for which the quadratic forms induced by the corresponding linear matrix combinations are nonnegative over the nonnegative orthant. Given a linear copositive problem, we define immobile indices of its constraints and a normalized immobile index set. We prov...

WGSCO 2018, Workshop on Graph Spectra, Combinatorics and Optimization was
successfully held in the University of Aveiro, Portugal, at the occasion of the 65th
birthday of Professor Domingos M. Cardoso.
The topics of the Workshop reflected the diversity of the scientific interests of
Prof. Domingos M. Cardoso and the main lines of research of the Gr...

We consider a special class of optimization problems where the objective function is linear w.r.t. decision variable х and the constraints are linear w.r.t. х and quadratic w.r.t. index t defined in a given cone. The problems of this class can be considered as a generalization of semi-definite and copositive programming problems. For these problems...

This special issue of Discrete Applied Mathematics (DAM) is based on the contributions presented at the Workshop on
Graph Spectra, Combinatorics and Optimization (WGSCO2018) held in Aveiro, Portugal, 25–27 January 2018, on occasion
of the 65th birthday of Professor Domingos M. Cardoso.
The Workshop counted with 8 invited plenary talks, 80 contribut...

The concepts of immobile indices and their immobility orders are objective and important characteristics of feasible sets of semi-infinite programming (SIP) problems. They can be used for the formulation of new efficient optimality conditions without constraint qualifications. Given a class of convex SIP problems with polyhedral index sets, we desc...

This book constitutes revised and selected papers from the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekaterinburg, Russia, in July 2019.
The 40 full papers and 4 short papers presented in this volume were carefully reviewed and selected from a total of 170 submissions. The paper...

In the present paper, we apply our recent results on optimality for convex semi-infinite programming to a problem of linear copositive programming (LCP). We prove explicit optimality conditions that use concepts of immobile indices and their immobility orders and do not require the Slater constraint qualification to be satisfied. The only assumptio...

The paper is devoted to study of a special class of semi-infinite problems arising in nonlinear parametric optimization. These semi-infinite problems are convex and possess noncompact index sets. In the paper, we present conditions, which guarantee the existence of optimal solutions, and prove new optimality criterion. An example illustrating the o...

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...

We consider a special Nonlinear Programming problem depending on integer parameters. For some values of these parameters (the "right" ones), this problem satisfies certain properties used in study of differential properties of optimal solutions in parametric Semi-Infinite Programming. We deduce the conditions guaranteing the existence of the "right...

We consider a mechanical problem concerning a 2D axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry. The body moves through a medium of non-interacting particles at rest, and collisions of particles with the body's boundary are perfectly elastic (billiard-like). The body has a blunt nos...

The paper deals with a nonlinear programming (NLP) problem that depends on a finite number of integers (parameters). This problem has a special form, and arises as an auxiliary problem in study of solutions' properties of parametric semi-infinite programming (SIP) problems with finitely representable compact index sets. Therefore, it is important t...

We introduce hybrid stochastic differential equations with jumps and to its optimal control. These hybrid systems allow for the representation of “random” and impulsive regime switches or paradigm shifts in economies and societies, and they are of growing importance in the areas of finance, science, development and engineering. We present special a...

In the paper, we consider a problem of convex Semi-Infinite Programming with a compact index set defined by a finite number of nonlinear inequalities. While studying this problem, we apply the approach developed in our previous works and based on the notions of immobile indices, the corresponding immobility orders and the properties of a specially...

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.

Hosted by the University of Aveiro, Portugal, the XXX EURO mini
conference on “Optimization in the Natural Sciences” (MEC
XXX) was held from February 5 to 9 through the support of the,
Association of European Operations Research Societies (EURO) and
EURO Working Group on Continuous Optimization (EUROPT).
Conference topics reflected the diversity of...

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;25:279–2...

We consider a convex problem of Semi-Infinite Programming (SIP) with a multidimensional index set defined by a finite number
of box constraints. In study of this problem we apply the approach suggested in Kostyukova et al. (Int. J. Math. Stat. 13(J08):13–33,
2008) for convex SIP problems with one-dimensional index sets and based on the notions of i...

We consider two closely related optimization problems: a problem of convex semi-infinite programming with multidimensional index set and a linear problem of semi-definite programming. In the study of these problems we apply the approach suggested in our recent paper [14] and based on the notions of immobile indices and their immobility orders. For...

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 d...

A food bank is a non-profit, social solidarity organization that typically distributes the donated food among a wide variety of local non-profit, social solidarity institutions that 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 do...

We study the Magnus effect: deflection of the trajectory of a spin- ning body moving in a medium. The body is rough; that is, there are small cavities on its surface. We concentrate on the extreme case of rare medium, where mutual interaction of the medium particles is neglected and reflections of the particles from the body's surface are elastic....

We state a new implicit optimality criterion for convex semi-infinite programming (SIP) problems. This criterion does not
require any constraint qualification and is based on concepts of immobile index and immobility order. Given a convex SIP problem
with a continuum of constraints, we use an information about its immobile indices to construct a no...

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 a...

We consider convex problems of semi-infinite programming (SIP) using an approach based on the implicit optimality criterion.
This criterion allows one to replace optimality conditions for a feasible solution x
0 of the convex SIP problem by such conditions for x
0 in some nonlinear programming (NLP) problem denoted by NLP(I(x
0)). This nonlinear pr...

Pressure force exerted on a rough disk spinning in a flow of noninteracting particles is determined by considering that a flow of point particles impinges on a body spinning around a fixed point. The rough disk is identical with the sequence of sets and thus the sets can be viewed as successive approximations of the rough disk. A proper choice of s...

Some references:
G.-W. Weber, P. Taylan, B. Akteke-Öztürk and Ö. Ugur, Mathematical and data mining contributions to dynamics and optimization of gene-environment networks, invited paper, in the special issue "Interdisciplinary Applications in Physics: Complexity in Social and Biological Systems" of Electronic Journal of Theoretical Physics (EJTP)...

Optimization is an area of mathematics that finds an optimum (minimum or maximum) of some function defined in a finite or infinite set. If the functions used for the problem formulation are continuous or piece- wise continuous, we obtain a continuous optimization problem. When some practical task is formulated in the form of optimization problem, t...

A spinning rough disk moves through a rarefied medium on the plane. The roughness is formed by small cavities on the disk boundary. The medium is so rare that mutual interaction of particles can be neglected. All collisions of particles with the disk are perfectly elastic; there may happen multiple collisions in the cavities. We calculate the force...

We consider convex Semi-Infinite Programming (SIP) problems with a continuum of constraints. For these problems we introduce new concepts of immobility orders and immobile indices. These concepts are objective and important characteristics of the feasible sets of the convex SIP problems since they make it possible to formulate optimality conditions...

Generally speaking, an optimization problem consists in maximization or minimization of some function (objective function) f:S→ℝ. The feasible set S⊆ℝ n 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 ℝ n . The methods...

Optimality conditions for nonlinear problems with equality and inequality constraints are considered. In the case when no constraint qualification (or regularity) is assumed, the Lagrange multiplier corresponding to the objective function can vanish in first order necessary optimality conditions given by Fritz John and the corresponding extremum is...

We present a constructive approach to solving convex programming problems in separable form and new constructive methods for simultaneously solving pairs of primal and dual geometric programming problems. These methods are based on the new principle of accumulation of approximate functions, which involves an approximation of the objective functions...

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...

We study abnormal extremum in the problem of non-linear pro-gramming with mixed constraints. Abnormal extremum occurs when in necessary optimality conditions the Lagrange multiplier, which cor-responds to the objective function, vanishes. We demonstrate that in this case abnormal second-order sufficient optimality conditions guar-antee rigidity of...

## Projects

Projects (3)

The EURO WISDOM Research subcommittee is working on research to support, empower, and encourage the participation of all genders in Operational Research.