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The Eighth Congress of Romanian Mathematicians |
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List of talks
Special session: Local rings and homological algebra. Special session dedicated to Prof. Nicolae Radu
II. Algebraic, Complex and Differential Geometry and Topology
Special session: Geometry and Topology of Differentiable Manifolds and Algebraic Varieties
III. Real and Complex Analysis, Potential Theory
IV. Ordinary and Partial Differential Equations, Variational Methods, Optimal Control
Special session: Optimization and Games Theory
V. Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics
Special session: Spectral Theory and Applications in Mathematical Physics
Special session: Dynamical Systems and Ergodic Theory
VI. Probability, Stochastic Analysis, and Mathematical Statistics
VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences
Special session: Mathematical Modeling of Some Medical and Biological Processes
Special session: Mathematical Models in Astronomy
VIII. Theoretical Computer Science, Operations Research and Mathematical Programming
Special session: Logic in Computer Science
IX. History and Philosophy of Mathematics
Optimization and Games Theory (special session)
(this list is in updating process)
1.
BOT Radu Ioan radu.bot@univie.ac.at
University of Vienna, Austria
Title: Primal-dual algorithms for complexly structured nonsmooth convex optimization problems (details)
University of Vienna, Austria
Title: Primal-dual algorithms for complexly structured nonsmooth convex optimization problems (details)
Abstract:
In this talk we address the solving of a primal-dual pair of convex optimization problems with complex and intricate structures, by actually solving the corresponding system of optimality conditions, which involves mixtures of linearly composed, Lipschitz single-valued and parallel-sum type monotone operators. The proposed numerical schemes have as common feature the fact that the set-valued maximally monotone operators are processed individually via backward steps, while the single-valued ones are evaluated via explicit forward steps. The performances of the primal-dual algorithms are illustrated by numerical experiments on real-life problems arising in image and video processing, optimal portfolio selection and machine learning.
In this talk we address the solving of a primal-dual pair of convex optimization problems with complex and intricate structures, by actually solving the corresponding system of optimality conditions, which involves mixtures of linearly composed, Lipschitz single-valued and parallel-sum type monotone operators. The proposed numerical schemes have as common feature the fact that the set-valued maximally monotone operators are processed individually via backward steps, while the single-valued ones are evaluated via explicit forward steps. The performances of the primal-dual algorithms are illustrated by numerical experiments on real-life problems arising in image and video processing, optimal portfolio selection and machine learning.
2.
CSETNEK Ernoe Robert ernoe.robert.csetnek@univie.ac.at
University of Vienna, Austria
Title: An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions (details)
University of Vienna, Austria
Title: An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions (details)
Abstract:
We present a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.
We present a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.
3.
LOZOVANU Dmitrii dmitrii.lozovanu@math.md
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Republic of Moldova
Title: Determining the Saddle Points for Antagonistic Positional Games in Markov Decision Processes (details)
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Republic of Moldova
Title: Determining the Saddle Points for Antagonistic Positional Games in Markov Decision Processes (details)
Abstract:
A class of stochastic antagonistic positional games for Markov decision processes with average and expected total discounted costs optimization criteria are formulated and studied. Saddle point conditions in the considered class of games that extend saddle point conditions for deterministic parity games are derived. Furthermore algorithms for determining the optimal stationary strategies of the players are proposed and grounded.
A class of stochastic antagonistic positional games for Markov decision processes with average and expected total discounted costs optimization criteria are formulated and studied. Saddle point conditions in the considered class of games that extend saddle point conditions for deterministic parity games are derived. Furthermore algorithms for determining the optimal stationary strategies of the players are proposed and grounded.
4.
TKACENKO Alexandra alexandratkacenko@gmail.com
State University of Moldova, Republic of Moldova
Title: The fractional multi-objective transportation problem of fuzzy type. (details)
State University of Moldova, Republic of Moldova
Title: The fractional multi-objective transportation problem of fuzzy type. (details)
Abstract:
\documentclass[11pt, a4paper]{article} \begin{document} \title{The fractional multi-objective transportation problem of fuzzy type.} \author{Tkacenko Alexandra\\ Department of Applied Mathematics, Moldova State University\\ A. Mateevici str., 60, Chisinau, MD--2009, Moldova \\ alexandratkacenko@gmail.com} \date{} \maketitle In the paper is developed an iterative fuzzy programming approach for solving the multi-objective fractional transportation problem of "bottleneck" type [1] with some imprecise data. Minimizing the worst upper bound to obtain an efficient solution which is close to the best lower bound for each objective function iterative, we find the set of efficient solutions for all time levels [3]. The mathematical model of the proposed problem is the follows: \begin{equation} \min Z^{k}=\displaystyle\frac{\sum\limits_{i=1}^{m}\sum\limits_{i=1}^{n}\tilde{c}_{ij}^{k}x_{ij}}{\max\limits_{ij}\{t_{ij}\left| x_{ij}>0\}\right.} \end{equation} \begin{equation} \min Z^{k+1}=\max\limits_{ij}\{ t_{ij}\left|x_{ij}>0\right.\} \end{equation} \begin{equation} \sum\limits_{j=1}^{n}x_{ij}=a_{i}, \, i=1,2,\dots, m;\quad \, \sum\limits_{i=1}^{n} x_{ij}=a_{i}, j=1,2,\dots, n; \end{equation} \begin{equation} x_{ij}\ge 0,\, i=1,2,\dots,m,\, j=1,2,\dots,n,\, k=1,2,\dots ,r. \end{equation} where: $Z^{k}(x)=\left\{Z^{1}(x), Z^{2}(x),\dots, Z^{k}(x) \right\}$ is a vector of $r$ objective functions; $\tilde{c}_{ij}^{k} $ , k=1,2\dots r, i=1,2,\dots m, j=1,2,\dots n are unit costs or other amounts of fuzzy type, $ t_{ij} $ - necessary unit transportation time from source $i$ to destination $j$, $a_{i} $ - disposal at source i, $b_{j} $ -requirement of destination $j$, $x_{ij} $ - amount transported from source $i$ to destination $j$. In order to solve the model (1)-(4) we proposed to reduce it to one of linear type, equivalent in terms of the set of solutions. Since the parameters and coefficients of transportation multi-criteria models have real practical significances such as unit prices, unit costs and many other, all of them are interconnected with the same parameter of variation, which can be calculated by applying of various statistical methods. Thus, the model (1)-(4) can be transformed in one with deterministic type of data. It can be solved using fuzzy techniques: \begin{equation} \mu_{k}(Z^{k}))=\left\{ \begin{array}{ccc}1, \textrm{if } Z^{k}(x)\le L_k\\ \displaystyle\frac{U_k-Z^{k}(x)}{U_k-L_k},\, \textrm{if}, \, L_k
\documentclass[11pt, a4paper]{article} \begin{document} \title{The fractional multi-objective transportation problem of fuzzy type.} \author{Tkacenko Alexandra\\ Department of Applied Mathematics, Moldova State University\\ A. Mateevici str., 60, Chisinau, MD--2009, Moldova \\ alexandratkacenko@gmail.com} \date{} \maketitle In the paper is developed an iterative fuzzy programming approach for solving the multi-objective fractional transportation problem of "bottleneck" type [1] with some imprecise data. Minimizing the worst upper bound to obtain an efficient solution which is close to the best lower bound for each objective function iterative, we find the set of efficient solutions for all time levels [3]. The mathematical model of the proposed problem is the follows: \begin{equation} \min Z^{k}=\displaystyle\frac{\sum\limits_{i=1}^{m}\sum\limits_{i=1}^{n}\tilde{c}_{ij}^{k}x_{ij}}{\max\limits_{ij}\{t_{ij}\left| x_{ij}>0\}\right.} \end{equation} \begin{equation} \min Z^{k+1}=\max\limits_{ij}\{ t_{ij}\left|x_{ij}>0\right.\} \end{equation} \begin{equation} \sum\limits_{j=1}^{n}x_{ij}=a_{i}, \, i=1,2,\dots, m;\quad \, \sum\limits_{i=1}^{n} x_{ij}=a_{i}, j=1,2,\dots, n; \end{equation} \begin{equation} x_{ij}\ge 0,\, i=1,2,\dots,m,\, j=1,2,\dots,n,\, k=1,2,\dots ,r. \end{equation} where: $Z^{k}(x)=\left\{Z^{1}(x), Z^{2}(x),\dots, Z^{k}(x) \right\}$ is a vector of $r$ objective functions; $\tilde{c}_{ij}^{k} $ , k=1,2\dots r, i=1,2,\dots m, j=1,2,\dots n are unit costs or other amounts of fuzzy type, $ t_{ij} $ - necessary unit transportation time from source $i$ to destination $j$, $a_{i} $ - disposal at source i, $b_{j} $ -requirement of destination $j$, $x_{ij} $ - amount transported from source $i$ to destination $j$. In order to solve the model (1)-(4) we proposed to reduce it to one of linear type, equivalent in terms of the set of solutions. Since the parameters and coefficients of transportation multi-criteria models have real practical significances such as unit prices, unit costs and many other, all of them are interconnected with the same parameter of variation, which can be calculated by applying of various statistical methods. Thus, the model (1)-(4) can be transformed in one with deterministic type of data. It can be solved using fuzzy techniques: \begin{equation} \mu_{k}(Z^{k}))=\left\{ \begin{array}{ccc}1, \textrm{if } Z^{k}(x)\le L_k\\ \displaystyle\frac{U_k-Z^{k}(x)}{U_k-L_k},\, \textrm{if}, \, L_k
5.
UNGUREANU Valeriu v.a.ungureanu@gmail.com
State University of Moldova, Republic of Moldova
Title: Strategic Games, Information Leaks, Corruption, and Solution Principles (details)
State University of Moldova, Republic of Moldova
Title: Strategic Games, Information Leaks, Corruption, and Solution Principles (details)
Abstract:
We consider strategic games with rules violated by information leaks (corruption of simultaneity). As a result of corruption, various para/pseudo sequential games appear. The classification of such games is provided on the base of the applicable solution principles. Conditions for solution existence are highlighted, formulated and analysed.
We consider strategic games with rules violated by information leaks (corruption of simultaneity). As a result of corruption, various para/pseudo sequential games appear. The classification of such games is provided on the base of the applicable solution principles. Conditions for solution existence are highlighted, formulated and analysed.
6.
VOISEI Mircea mvoisei@towson.edu
Towson University, Towson, Maryland - 21208, U.S.A.
Title: The local equicontinuity of a maximal monotone operator and consequences (details)
Towson University, Towson, Maryland - 21208, U.S.A.
Title: The local equicontinuity of a maximal monotone operator and consequences (details)
Abstract:
The local equicontinuity of an operator $T:Xrightrightarrows X^{*}$ with proper Fitzpatrick function $varphi_{T}$ and defined in a barreled locally convex space $X$ has been shown to hold on the algebraic interior of operatorname*{Pr}_{X}(operatorname*{dom}varphi_{T})$)% footnote{see cite[Theorem 4]{MR3252437}% }. The current note presents direct consequences of the aforementioned result with regard to the local equicontinuity of a maximal monotone operator defined in a barreled locally convex space including a new proof of James's Theorem and the universality of the normal cone in the sum theorem for maximal monotone operators.
The local equicontinuity of an operator $T:Xrightrightarrows X^{*}$ with proper Fitzpatrick function $varphi_{T}$ and defined in a barreled locally convex space $X$ has been shown to hold on the algebraic interior of operatorname*{Pr}_{X}(operatorname*{dom}varphi_{T})$)% footnote{see cite[Theorem 4]{MR3252437}% }. The current note presents direct consequences of the aforementioned result with regard to the local equicontinuity of a maximal monotone operator defined in a barreled locally convex space including a new proof of James's Theorem and the universality of the normal cone in the sum theorem for maximal monotone operators.