Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations

AMS Subj. Classification: 49J15, 49M15

Optimal Choice of a Firm in Conducting Auction

Силвия К. Баева, Цветана Хр. Недева - Важен аспект в системата на Министерството на регионалното развитие и благоустройство е работата по Оперативна програма “Регионално развитие” с приоритетна ос “Устойчиво и интегрирано градско развитие” по операция “Подобряване на физическата среда и превенция на риска”. По тази програма са включени 86 общини. Финансовият ресурс на тази операция е на стойност 238 589 939 евро, от които 202 801 448 евро са европейско финансиране [1]. Всяка от тези 86 общини трябва да реши задачата за възлагане на обществена поръчка на определена фирма по тази операция. Всъщност, тази задача е задача за провеждане на общински търг за избор на фирма-изпълнител. Оптималният избор на фирма-изпълнител е много важен. Задачата за провеждане на търг ще формулираме като задача на многокритериалното вземане на решения, като чрез подходящо изграждане на критерии и методи може да се трансформира до задача на еднокритериалната оптимизация.

Optimal Control of Heterogeneous Systems

Цветомир Цачев - В настоящия доклад се прави преглед на някои резултати от областта на оптималното управление на непрекъснатите хетерогенни системи, публикувани в периодичната научна литература в последните години. Една динамична система се нарича хетерогенна, ако всеки от нейните елементи има собствена динамиката. Тук разглеждаме оптимално управление на системи, чиято хетерогенност се описва с едномерен или двумерен параметър – на всяка стойност на параметъра отговаря съответен елемент на системата. Хетерогенните динамични системи се използват за моделиране на процеси в икономиката, епидемиологията, биологията, опазване на обществената сигурност (ограничаване на използването на наркотици) и др. Тук разглеждаме модел на оптимално инвестиране в образование на макроикономическо ниво [11], на ограничаване на последствията от разпространението на СПИН [9], на пазар на права за въглеродни емисии [3, 4] и на оптимален макроикономически растеж при повишаване на нивото на върховите технологии [1]. Ключови думи: оптимално управление, непрекъснати хетерогенни динамични системи, приложения в икономиката и епидемиолегията

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

On the k-anonymization of time-varying and multi-layer social graphs

The popularity of online social media platforms provides an unprecedented opportunity to study real-world complex networks of interactions. However, releasing this data to researchers and the public comes at the cost of potentially exposing private and sensitive user information. It has been shown that a naive anonymization of a network by removing the identity of the nodes is not sufficient to preserve users’ privacy. In order to deal with malicious attacks, k -anonymity solutions have been proposed to partially obfuscate topological information that can be used to infer nodes’ identity. In this paper, we study the problem of ensuring k anonymity in time-varying graphs, i.e., graphs with a structure that changes over time, and multi-layer graphs, i.e., graphs with multiple types of links. More specifically, we examine the case in which the attacker has access to the degree of the nodes. The goal is to generate a new graph where, given the degree of a node in each (temporal) layer of the graph, such a node remains indistinguishable from other k-1 nodes in the graph. In order to achieve this, we find the optimal partitioning of the graph nodes such that the cost of anonymizing the degree information within each group is minimum. We show that this reduces to a special case of a Generalized Assignment Problem, and we propose a simple yet effective algorithm to solve it. Finally, we introduce an iterated linear programming approach to enforce the realizability of the anonymized degree sequences. The efficacy of the method is assessed through an extensive set of experiments on synthetic and real-world graphs.

Integrated optimisation of surface roughness and tool performance when face milling 416 SS

Tool life is an important factor to be considered during the optimisation of a machining process since cutting parameters can be adjusted to optimise tool changing, reducing cost and time of production. Also the performance of a tool is directly linked to the generated surface roughness and this is important in cases where there are strict surface quality requirements. The prediction of tool life and the resulting surface roughness in milling operations has attracted considerable research efforts. The research reported herein is focused on defining the influence of milling cutting parameters such as cutting speed, feed rate and axial depth of cut, on three major tool performance parameters namely, tool life, material removal and surface roughness. The research is seeking to define methods that will allow the selection of optimal parameters for best tool performance when face milling 416 stainless steel bars. For this study the Taguchi method was applied in a special design of an orthogonal array that allows studying the entire parameter space with only a number of experiments representing savings in cost and time of experiments. The findings were that the cutting speed has the most influence on tool life and surface roughness and very limited influence on material removal. By last tool life can be judged either from tool life or volume of material removal.

Variable Neighborhood Search for Solving the Capacitated Single Allocation Hub Location Problem

In this paper a Variable Neighborhood Search (VNS) algorithm for solving the Capacitated Single Allocation Hub Location Problem (CSAHLP) is presented. CSAHLP consists of two subproblems; the first is choosing a set of hubs from all nodes in a network, while the other comprises finding the optimal allocation of non-hubs to hubs when a set of hubs is already known. The VNS algorithm was used for the first subproblem, while the CPLEX solver was used for the second. Computational results demonstrate that the proposed algorithm has reached optimal solutions on all 20 test instances for which optimal solutions are known, and this in short computational time.

Optimal investment under stochastic volatility and power type utility function

2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.

Wealth shocks, credit-supply shocks, and asset allocation:evidence from household and firm portfolios

We use a unique dataset with bank clients’ security holdings for all German banks to examine how macroeconomic shocks affect asset allocation preferences of households and non-financial firms. Our analysis focuses on two alternative mechanisms which can influence portfolio choice: wealth shocks, which are represented by the sovereign debt crisis in the Eurozone, and credit-supply shocks which arise from reductions in borrowing abilities during bank distress. We document het- erogeneous responses to these two types of shocks. While households with large holdings of secu- rities from stressed Eurozone countries (Greece, Ireland, Italy, Portugal, and Spain) decrease the degree of concentration in their security portfolio as a result of the Eurozone crisis, non-financial firms with similar levels of holdings from stressed Eurozone countries do not. Credit-supply shocks at the bank level (caused by bank distress) result in lower concentration, for both households and non-financial corporations. We also show that only shocks to corporate credit bear ramifications on bank clients’ portfolio concentration, while shocks in retail credit are inconsequential. Our results are robust to falsification tests, propensity score matching techniques, and instrumental variables estimation.

What counts versus what can be counted:the complex interplay of market orientation and marketing performance measurement

Market orientation (MO) and marketing performance measurement (MPM) are two of the most widespread strategic marketing concepts among practitioners. However, some have questioned the benefits of extensive investments in MO and MPM. More importantly, little is known about which combinations of MO and MPM are optimal in ensuring high business performance. To address this research gap, the authors analyze a unique data set of 628 firms with a novel method of configurational analysis: fuzzy-set qualitative comparative analysis. In line with prior research, the authors find that MO is an important determinant of business performance. However, to reap its benefits, managers need to complement it with appropriate MPM, the level and focus of which vary across firms. For example, whereas large firms and market leaders generally benefit from comprehensive MPM, small firms may benefit from measuring marketing performance only selectively or by focusing on particular dimensions of marketing performance. The study also finds that many of the highest-performing firms do not follow any of the particular best practices identified.

Optimal combination of energy crops under different policy scenarios:the case of Northern Greece

Energy crops production is considered as environmentally benign and socially acceptable, offering ecological benefits over fossil fuels through their contribution to the reduction of greenhouse gases and acidifying emissions. Energy crops are subjected to persistent policy support by the EU, despite their limited or even marginally negative impact on the greenhouse effect. The present study endeavors to optimize the agricultural income generated by energy crops in a remote and disadvantageous region, with the assistance of linear programming. The optimization concerns the income created from soybean, sunflower (proxy for energy crop), and corn. Different policy scenarios imposed restrictions on the value of the subsidies as a proxy for EU policy tools, the value of inputs (costs of capital and labor) and different irrigation conditions. The results indicate that the area and the imports per energy crop remain unchanged, independently of the policy scenario enacted. Furthermore, corn cultivation contributes the most to iFncome maximization, whereas the implemented CAP policy plays an incremental role in uptaking an energy crop. A key implication is that alternative forms of motivation should be provided to the farmers beyond the financial ones in order the extensive use of energy crops to be achieved.

Közjavak optimális előállítása (Optimal production of public goods)

A közjavak közgazdaságilag optimális szintjének előállítása piaci körülmények között általában nehézségekbe ütközik. Napjainkban számos országban többféle közjószág áll rendelkezésre, a szakirodalomban pedig például a nyugdíjrendszer egyes elemeinek közjószágjellegével kapcsolatos felvetések is megjelentek már. Ezzel összefüggésben is érdekes a kérdés, milyen körülmények között fordulhat elő, hogy racionális egyéni döntéshozók egyénileg optimális döntéseikkel valamely közjószág optimális szintjét hozzák létre. Jelen tanulmány ezzel a kérdéssel foglalkozik. / === / It is difficult to produce the economically optimal level of public goods in a market environment. There are many different types of public goods, and today even some aspects of the pension system are considered as such. Still, it is an interesting question if individually optimal decisions made by rational individuals could lead to an optimal level of public goods. The paper attempts to analyze this question.

On optimal completions of incomplete pairwise comparison matrices

An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uniqueness problem of the best completion for two weighting methods, the Eigen-vector Method and the Logarithmic Least Squares Method. In both settings we obtain the same simple graph theoretic characterization of the uniqueness. The optimal completion will be unique if and only if the graph associated with the partially defined matrix is connected. Some numerical experiences are discussed at the end of the paper.

Többéves pénzügyi keret vitája középről és a sor végéről – Magyarország és Lettország harcban a mezőgazdasági és kohéziós támogatásokért (Debate on the eu multiannual financial framework from the view of Hungary and Latvia)

Az Európai Bizottság 2011. júniusban nyilvánosságra hozott, a következő hétéves időszakot meghatározó pénzügyi keretéről szóló javaslatával elindult a tagállamok, illetve az intézmények közötti szakmai és politikai érvelés, az alkudozások sora. A két legfontosabb költségvetési tétel, a mezőgazdasági támogatások és a kohéziós források előnyös allokációja Magyarország és Lettország számára is kiemelt prioritás. A tárgyalások során Lettország érdeke az alacsony közvetlen mezőgazdasági támogatások emelése, míg Magyarország kedvező pozíciójának megtartásáért harcol. A kohéziós politikára tett Bizottsági javaslat mindkét ország számára hátrányos, így közös érdek a források összegének szinten tartása és a kedvezőtlen támogatási felső határ emelése. ______ Following the European Commission’s proposal on the next Multiannual Financial Framework was published in June 2011, tense debate started to defend national priorities. The proper allocation of the agricultural and cohesion founds is essential for both, Hungary and Latvia as well. Latvia’s objectives is to introduce fair direct payments to farmers, stipulating that the lowest payments must constitute at least 80 per cent of the average amount of the EU direct payments, while Hungary tries to defend its relatively favourable position by receiving almost the amount of the EU average. Common interest for Hungary and for Latvia in the EU budget talks is to retain cohesion financing at least at the current level and to change the unfavourable proposal on capping.