Static synchronous compensation (StatCom) is an application that utilizes a voltage source converter (VSC) to provide instantaneous reactive power support to the connected power system. Conventionally, StatComs are employed for reactive power support only. However, with the integration of energy storage (ES) into a StatCom, it can provide active power support in addition to the reactive power support. This thesis deals with the integration of ES into StatComs. The investigation involves the following aspects: possible benefits for power systems, main circuit design, and control strategies. As the basis of the investigation, a control scheme is proposed for two-level VSCs. It is a novel flux modulation scheme combined with the well-known deadbeat current control. The current controller is capable of controlling the positive sequence, the negative sequence, and the offset components of the converter current. With flux modulation, all the three above-mentioned components of the bus flux are controllable. This differs from the conventional voltage modulation scheme, in which only the positive and negative sequence components of the bus voltage are controllable. The difference between the proposed flux modulation scheme and the voltage modulation scheme is investigated regarding saturation of transformers in the connected system during fault recovery. The investigation shows that by controlling the offset component of the bus flux, the transformer saturation problem can be mitigated to a certain extent. The possible benefits of the additional active power support of StatComs are investigated through several case studies. Different active power compensation schemes are proposed. First, active power compensation for sudden load changes in weak systems is investigated. The proposed control strategies are verified through computer simulations and through experiments in a real-time simulator. It is shown that with active power compensation, both the phase jumps and magnitude variations in the voltage at the PCC can be reduced significantly. Secondly, the power compensation of cyclic loads is investigated. The results show that the power quality at the connection point can be improved regarding both phase jumps and magnitude variations. In the third case study, the fault-recovery performance of an example system is investigated, showing that improved performance can be achieved by the additional active power support. ES devices such as capacitors, supercapacitors, and batteries exhibit considerable variation in the terminal voltage during a charging/discharging cycle. A direct connection of ES devices to the dc side of a VSC requires a higher voltage rating of the VSC. Thus, the cost of the VSC has to be increased. In this thesis, a dual thyristor converter topology is proposed to interface ES devices with the dc side of the VSC. First, a cost comparison is performed to compare the total cost of the whole system with and without the proposed interface topology. A cost comparison between various types of ES is also presented, providing a guideline for the choice of ES at energy levels where several alternatives exist. Then, the dynamics of systems with the proposed interface topology are investigated. Control strategies are proposed and verified by computer simulations. Two different control methods for the dual-thyristor converter are compared. / QC 20100819

The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. This notion offers a way tounderstand the efficiency of different numerical methods. The first paper develops new expansions of the weakcomputational error for Itˆo stochastic differentialequations using Malliavin calculus. These expansions have acomputable leading order term in a posteriori form, and arebased on stochastic flows and discrete dual backward problems.Beside this, these expansions lead to efficient and accuratecomputation of error estimates and give the basis for adaptivealgorithms with either deterministic or stochastic time steps.The second paper proves convergence rates of adaptivealgorithms for Itˆo stochastic differential equations. Twoalgorithms based either on stochastic or deterministic timesteps are studied. The analysis of their numerical complexitycombines the error expansions from the first paper and anextension of the convergence results for adaptive algorithmsapproximating deterministic ordinary differential equations.Both adaptive algorithms are proven to stop with an optimalnumber of time steps up to a problem independent factor definedin the algorithm. The third paper extends the techniques to theframework of Itˆo stochastic differential equations ininfinite dimensional spaces, arising in the Heath Jarrow Mortonterm structure model for financial applications in bondmarkets. Error expansions are derived to identify differenterror contributions arising from time and maturitydiscretization, as well as the classical statistical error dueto finite sampling. The last paper studies the approximation of linear ellipticstochastic partial differential equations, describing andanalyzing two numerical methods. The first method generates iidMonte Carlo approximations of the solution by sampling thecoefficients of the equation and using a standard Galerkinfinite elements variational formulation. The second method isbased on a finite dimensional Karhunen- Lo`eve approximation ofthe stochastic coefficients, turning the original stochasticproblem into a high dimensional deterministic parametricelliptic problem. Then, adeterministic Galerkin finite elementmethod, of either h or p version, approximates the stochasticpartial differential equation. The paper concludes by comparingthe numerical complexity of the Monte Carlo method with theparametric finite element method, suggesting intuitiveconditions for an optimal selection of these methods. 2000Mathematics Subject Classification. Primary 65C05, 60H10,60H35, 65C30, 65C20; Secondary 91B28, 91B70. / QC 20100825

This thesis consists of a summary and four scientific articles. All four articles consider various aspects of stochastic differential equations and the purpose of the summary is to provide an introduction to this subject and to supply the notions required in order to fully understand the articles. In the first article we conduct a thorough study of the multi-dimensional Skorohod problem in time-dependent domains. In particular we prove the existence of cádlág solutions to the Skorohod problem with oblique reflection in time-independent domains with corners. We use this existence result to construct weak solutions to stochastic differential equations with oblique reflection in time-dependent domains. In the process of obtaining these results we also establish convergence results for sequences of solutions to the Skorohod problem and a number of estimates for solutions, with bounded jumps, to the Skorohod problem. The second article considers the problem of determining the sensitivities of a solution to a second order parabolic partial differential equation with respect to perturbations in the parameters of the equation. We derive an approximate representation of the sensitivities and an estimate of the discretization error arising in the sensitivity approximation. We apply these theoretical results to the problem of determining the sensitivities of the price of European swaptions in a LIBOR market model with respect to perturbations in the volatility structure (the so-called ‘Greeks’). The third article treats stopped diffusions in time-dependent graph domains with low regularity. We compare, numerically, the performance of one adaptive and three non-adaptive numerical methods with respect to order of convergence, efficiency and stability. In particular we investigate if the performance of the algorithms can be improved by a transformation which increases the regularity of the domain but, at the same time, reduces the regularity of the parameters of the diffusion. In the fourth article we use the existence results obtained in Article I to construct a projected Euler scheme for weak approximation of stochastic differential equations with oblique reflection in time-dependent domains. We prove theoretically that the order of convergence of the proposed algorithm is 1/2 and conduct numerical simulations which support this claim.

All'inizio del xxi secolo la crescita economica e politica della repubblica popolare cinese è la più dinamica nel sistema internazionale. Mediante un'analisi della transizione che il sistema stesso sta attraversando, e utilizzando una varietà di indicatori (relazioni multilaterali/bilaterali, comportamento di voto in sede gnu, influenza nella periferia del sistema, evoluzione interna), questo lavoro tenta di cartografare il nuovo ruolo giocato dalla Cina sulla scena politica globale. / At the dawn of the xxi century, the people's republic of China's growth in economic and political influence is the most striking phenomenon in the international system. coupling an analysis of the changes that the system itself is undergoing with a variety of country-specific indicators (multilateral/bilateral relations, voting behaviour at the UN, activities in the periphery of the system, internal dynamics), this work aims at mapping the new role played by China in the international system.

Designingenjörsstudenterna, Pedersen och Birkehag, på Högskolan i Skövde har i samarbete med hjälpmedelsföretaget Handicare AB arbetat med ett produktutvecklingsprojekt under våren 2012. Projektets syfte var att uppgradera företagets befintliga produkt QuickMove som är ett uppresning- och förflyttningshjälpmedel inom vården. Målet var att bibehålla QuickMoves funktioner och säkerhet samt skapa innovativa lösningar och minska transport- och tillverkningskostnader. Produktutvecklingsprocessen skedde iterativt och började med kundundersökningar i form av enkäter, intervjuer och fokusgrupper. Med hjälp av detta gjordes en kundkravsspecifikation som under hela projektet fanns nära till hands. Därefter påbörjades idégenereringen med hjälp av diverse kreativitetsmetoder. En fullskalig modell byggdes därefter i VP-rör och silvertejp. Utvärderingar och tester gjordes på modellen som därefter kunde vidareutvecklas och modelleras i programvaran SolidWorks. Hållfasthetsberäkningar, materialval, tillverkningsmetoder, formspråk, kostnader och ergonomi var områden som arbetades med och ett slutkoncept fastställdes. Resultatet bestod av ett uppgraderat hjälpmedel som fick namnet UpAway. Hjälpmedlets fraktvolym kommer att minska med 75 procent och produkten har färre antal delar jämfört med QuickMove. UpAways nya genomarbetade design och funktionella anpassningar kommer leda till fler nya användargrupper både inom Sverige och internationellt/globalt. Enligt studenternas bedömning har UpAway alla förutsättningar till en bredare marknad. / During the Spring of 2012 Pedersen and Birkehag, two product design engineering students at University of Skövde, carried out a product development project in cooperation with Handicare AB. The aim of the project was to upgrade QuickMove, the current standing-up and transfer aid used in health care and developed by Handicare. The goal of the project was to maintain the functions and safety features of QuickMove while creating new innovative solutions and lowering the transportation and manufacturing costs. The product development process was iterative and started with the research of customer requirements, which involved user studies and interviews. The customer requirements specification is based on customers’ needs and was used as guideline throughout the product development process. Ideas and concepts were generated with various creativity methods. A full scale model was built with VP-pipe and duct tape. Evaluations and tests were performed on the model and further developments were carried out. To analyze the result a visual model was built with the software SolidWorks. Strength of materials analyses, material selection, development, design, cost and ergonomics were all taken in consideration and a final concept was elaborated. The result was an upgraded aid named UpAway. This aid contains fewer parts than QuickMove and will reduce transportation volume by 75 percent. The newly developed design of UpAway, adapted to customers’ demands, will generate customers’ interest and according the students thus result in a broader market both in Sweden and worldwide.

Changing trends in customer preference, competitors’ offerings, new technologies and development techniques may disrupt a firm from its current leading market position and may favor other firms that prioritize innovation. Once a market opportunity is identified (i.e., find an answer to the ‘what to do’ question), firms need to engage in a series of activities and information processing to determine an appropriate way to monetize that opportunity – that is, firms need to find an answer to the ‘how to do’ question. Alternately, a firm may first identify a technological opportunity (i.e. find an answer to the ‘how to do’) and then find a market opportunity (i.e. find an answer to the ‘what to do’ question) to make use of the technological opportunity. Two scales that measure the capabilities of firms to address the following two questions – ‘what to do’ and ‘how to do’ - were reported; these were labelled as market-scanning capability (MktScan) and technology-scanning capability (TechScan); and these two scales were also tested in a broader research model. In turbulent environments, marketing and R&D become more challenging, since they face an uncertain future. Firms need to learn systemic scanning and decoding of apparently random changes in their business environment and imagine a pattern that makes sense. One cannot plan for uncertainty. A better strategy is to be prepared for it. One way to prepare is to develop the capabilities that would help the firm to become more adaptive. Drucker (1992) also argued that instead of planning for the long term that is uncertain, firms needed to become adaptive to tackle uncertainty. The ability of a firm to adapt to the changes depends on its ability to sense the nature of the changes in its business environment and respond to those. Sense-and-respond framework (Haeckel 1999; Haeckel 2000; Day and Schoemaker 2006) was proposed to emphasize the identification of weak signals (Ansoff 1975) to tackle increased uncertainty in business environment. In current days, effectiveness of firm’s activities often depends on the richness of its sources of information and its capability to process the collected information to identify the patterns of change happening in its business environments. Information processing may happen in two dimensions: in market dimension and in technology dimension. Firms’ capabilities for information collecting and processing in these two dimensions were measured using two firm-level constructs. These are market-scanning capability and technology-scanning capability. Resource-based theory helped to understand how firms use their tangible and intangible resources to compete in the market. Specific problem-solving aspects of the processes, activities, and cultural norms enable firms to make decisions about engaging the available resources and capabilities in ways that maximize customer value, by realizing the identified opportunities into product and service offerings. This research identified the characteristic strength of this problem-solving approach of firms – collecting information both internally and externally about possible market opportunities and technological options, organization-wide processing of that information, and taking actions to respond using insights gained – as two latent constructs called ‘market-scanning capability’ and ‘technology-scanning capability’. The concepts of ‘market-scanning capability’ and ‘technology-scanning capability’ were first defined and then, scales were developed to enable researchers and managers to measure these firm-level constructs. Next, the predictive roles of these capabilities on firm performance were examined. Empirical analysis for scale development and validation of the research model were performed with data collected through a web-based survey of Canadian manufacturing firms. Firm performance was captured in two stages – first, by product innovation performance, and second, by overall firm performance. Product innovation performance was used as an intermediate performance measure to examine the direct influence on it of market-scanning capability and technology-scanning capability, and then, to relate product innovation performance to final business outcome measured using ‘overall firm performance’ scale. The study validated the notion of resource-based theory by supporting the belief that higher levels of market-scanning capability and technology-scanning capability would lead to improved product innovation performance. The role of environmental turbulence was also examined for its possible moderating effect. Two measures of environmental turbulence, namely, technology and market turbulence were used to test the moderation effect. The technology turbulence construct was found to have a moderating effect on the relationship between technology-scanning capability and product innovation performance, indicating that firms needed to focus more attention on the changes in the technology landscape when turbulence in the technological field was perceived to be higher, in order to keep the same level of product innovation performance. Insight gained from the study contributed to a knowledge-base that might be useful to both practitioners and researchers. The combination of TechScan and MktScan scales could be used as a benchmark tool by managers to assess firms’ readiness to take advantage of the opportunities that existed. On the theoretical side, the study contributed to the understanding by showing that both market-scanning capability and technology-scanning capability had direct and indirect influences on firm performance. Also, it was found that the indirect influence of a certain scanning capability became important when firms were pre-disposed to emphasize the other scanning capability.

Sammanfattning Titel:                                   Swot-modellen – Modellen, dess användning och användbarhet för framgångsrika företag i regionen   Nivå:                                  C-uppsats i ämnet företagsekonomi   Författare:                         Joachim Saillard   Handledare:                       Lars Torsten Eriksson   Datum:                               2012-07-16   Bakgrund:                          Swot-modellen ger en struktur för beskrivning och analys av en organisations starka samt svaga sidor, dess externa hot och möjligheter. Modellen har funnits i cirka 50 år och nått stor spridning. Vad har forskningen om swot-modellen hittills kommit fram till? Hur ser små- och medelstora företag i Gävleregionen på modellen i sina praktiker?   Syfte:                                  Syftet med uppsatsen är att göra en state-of-the-art genomgång av forskningen om swot-modellen samt visa hur en grupp regionala små- och medelstora företag använder modellen samt kritiskt testa Framför-databasens potential som empiriskt material. Avsikten är att lägga en grund samt skapa en utgångspunkt för fortsatt forskning om modellen som verktyg för företagsutveckling i den regionala miljön.                                             Metod:                                Studien bygger på en genomgång av ett stort antal forskningsartiklar om swot-modellen. De flesta artiklar analyserar enskilda aspekter av modellen, medan några visar sig ge en översikt över olika modellstudier. Eftersom det visar sig att ytterst få studier redovisar empiriska data om modellens användning och fortsatta empiriska studier behövs, har en genomgång också gjorts av swot-kommentarer i en databas för regionala företag – det så kallade Framför-projektet som drivs av bland annat Svenskt Näringsliv, Aktiv Revision och kommunerna i Gästrikland. I databasen finns registrerade data för små- och medelstora företag, åren 2002-2012. Databasen bygger på standardiserade intervjuer där svar registrerats om swot-data. Baserade på dessa har en sekundäranalys gjorts och den empiriska genomgången har behandlats som en pilotstudie om företags beskrivning av interna faktorer.   Resultat & slutsatser:       Studien ger en analys av forskningen om swot-modellen. Den visar att antalet teoretiska studier om swot-modellen ökat, medan få empiriska studier gjorts. Den empiriska delen visar att företagen i regel är väl förtrogna med modellen, men inte alltid har aktuella värden för dess huvudkategorier. Den aktuella databasen behöver förstärkas och modellen ges en bättre koppling till aktiv implementering.    Förslag till fortsatt forskning:                           Fortsatta studier behövs om företagens strategiska beslutssituationer utifrån swot-modellen som utvärderingsverktyg, och möjligen andra kompletterande teorier/modeller.   Uppsatsens bidrag:            Studien ger en överblick över den hittillsvarande forskningen om swot-modellen, dess användning och användbarhet för olika organisationer. Eftersom förvånansvärt få empiriska studier hittills gjorts kan uppsatsens empiriska studie ses som ett särskilt forskningsbidrag.   Nyckelord:                         Swot, företag, interna faktorer det vill säga starka och svaga sidor, strategisk planering, Framför-databasen, swot-modellens dualperspektiv. / Abstract Title:                                   The swot model – the model, its usage and usefulness for successful firms in the region   Level:                                 Final assignment for Bachelor Degree in Business Administration   Author:                               Joachim Saillard   Supervisor:                        Lars Torsten Eriksson   Date:                                  2012-07-16   Background:                      The swot-model provides a structure for description and analysis of an organizations strong and weak sides, its opportunities and threats. The model has existed approximately 50 years and has attained a big spread. What has the present research on swot concluded? How do small- and medium sized firms in the region of Gävle treat the model in their practices?   Aim:                                    The aim of the thesis is to do a state-of-the-art review on the research concerning the swot-model, and to show how a group of regional small- and medium sized firms use the model as well as to conduct a critical examination of the Framför-databases potential as empirical substance. The intention is to form a basis and starting point for future research, regarding to the model as a tool for business development in the regional environment.   Method:                             The study is founded on a review of a big number of research papers about the swot-model. Most of them analyze certain aspects of the model, while others seem to give a summary over different model studies. Since there has been shown to be exceedingly few studies who account for empirical data about the models use and further empirical studies is needed, a review of a database containing swot-comments – the so called Framför-project which is run by the Federation of Swedish Enterprise, Aktiv Revision and the municipalities in Gästrikland, has also been carried out. In the database there are registered data for small- and medium sized firms between the years 2002-2012. The database builds on standardized interviews of which swot-data have been registered. Based on this, secondary analysis has been carried out and the empirical review has been attended as a pilot study about firms’ descriptions of their internal factors.   Result & Conclusions:      The study provides an analyze on research concering the swot-model. It shows that the number of theoretical studies about the swot-model has increased, while few empirical studies have been carried out. The empirical part of the study shows that the firms generally are well familiar with the model, but that they don’t always have current values for its main categories. The current database needs to be strengthened and the model given a better connection to active realization.   Suggestions for future research:                 Future research is needed about the firms strategic decision situations with the swot-model as an evaluation tool as starting point, and possibly other complementing theories/models.   Contribution of the thesis:                          The thesis provides an overview over the research up until now concerning the swot-model, its use and usefulness for different organizations. Since surprisingly few present empirical studies have been carried out, the empirical study that the thesis provides can be seen as a particular research contribution.    Key words:                         Swot, firms, internal factors i.e. strong and weak sides, strategic planning, the Framför-database, swot-model dual perspective.

Dans la première partie de cette thèse nous appliquons le calcul via régularisation à l'étude d'un marché où le processus des prix d'un actif risqué n'est pas une semimartingale mais simplement à variation quadratique finie. Cette condition est réalisée lorsque le prix de l'actif est admis dans la classe A de toutes les stratégies admissibles, et devient réaliste si la condition de non-arbitrage sur l'ensemble de toutes les stratégies simples prévisibles n'est pas plausible. Cette situation est vérifiée, par exemple, lorsque l'agent est un initié ou si A est restreinte.<br />Nous fournissons des exemples de portefeuilles autofinancés et introduisons une notion de A-martingale. Un calcul relatif à celle-ci est développé. La condition de non-arbitrage parmi toutes les stratégies dans A est récupérée si le processus des prix de l'actif risqué est une A-martingale.<br />Nous abordons le problème de la viabilité du marché, de la couverture et de la maximisation de l'utilité de la richesse terminale.<br />La deuxième partie de la thèse est consacrée à l'étude d'une équation différentielle stochastique unidimensionnelle dirigée par une semimartingale mélangée à un processus à variation cubique finie.<br />Nous proposons une méthode qui repose sur une transformation réduisant le coefficient de diffusion à 1.<br />Le développement de la méthode utilisée nous conduit à des résultats significatifs dans l'analyse du calcul via régularisation.<br />En particulier, une formule de type Ito-Wentzell relative aux processus à variation cubique finie est<br />établie et la structure des processus weak-Dirichlet par rapport à la filtration brownienne est clarifiée.<br />Nous démontrons, par une approche similaire, l'existence et l'unicité d'une équation dirigée par un processus hölder-continu dans l'espace. En utilisant une formule d'Ito pour les semimartingales réversibles nous prouvons l'existence d'une solution lorsque le processus dirigeant l'équation est le mouvement brownien et le coefficient de diffusion est juste continu

The aim of this work is to make some investigations concerning duality for multiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, under some appropriate assumptions, the existence of strong duality. Closely related to the strong duality we derive the optimality conditions for each of these three duals. By means of these considerations, we study the duality for two vector optimization problems, namely, a convex multiobjective problem with cone inequality constraints and a special fractional programming problem with linear inequality constraints. To each of these vector problems we associate a scalar primal and study the duality for it. The structure of both scalar duals give us an idea about how to construct a multiobjective dual. The existence of weak and strong duality is also shown. We conclude our investigations by making an analysis over different duality concepts in multiobjective optimization. To a general multiobjective problem with cone inequality constraints we introduce other six different duals for which we prove weak as well as strong duality assertions. Afterwards, we derive some inclusion results for the image sets and, respectively, for the maximal elements sets of the image sets of these problems. Moreover, we show under which conditions they become identical. A general scheme containing the relations between the six multiobjective duals and some other duals mentioned in the literature is derived. / Das Ziel dieser Arbeit ist die Durchführung einiger Untersuchungen bezüglich der Dualität für Mehrzieloptimierungsaufgaben. Zu diesem Zweck wird als erstes mit Hilfe des so genannten konjugierten Verfahrens die Dualität für skalare Optimierungsaufgaben untersucht. Das erlaubt uns zu einer primalen Aufgabe drei unterschiedliche duale Aufgaben zuzuordnen. Wir betrachten die Beziehungen zwischen den optimalen Zielfunktionswerten der drei Dualaufgaben und untersuchen die Existenz der starken Dualität unter naheliegenden Annahmen. Im Zusammenhang mit der starken Dualität leiten wir für jede dieser Dualaufgaben die Optimalitätsbedingungen her. Die obengenannten Ergebnisse werden beim Studium der Dualität für zwei Vektoroptimierungsaufgaben angewandt, und zwar für die konvexe Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen und für eine spezielle Quotientenoptimierungsaufgabe mit linearen Ungleichungen als Nebenbedingungen. Wir assoziieren zu jeder dieser vektoriellen Aufgaben eine skalare Aufgabe für welche die Dualität betrachtet wird. Die Formulierung der beiden skalaren Dualaufgaben führt uns zu der Konstruktion der Mehrzieloptimierungsaufgabe. Die Existenz von schwacher und starker Dualität wird bewiesen. Wir schliessen unsere Untersuchungen ab, indem wir eine Analyse von verschiedenen Dualitätskonzepten in der Mehrzieloptimierung durchführen. Zu einer allgemeinen Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen werden sechs verschiedene Dualaufgaben eingeführt, für die sowohl schwache als auch starke Dualitätsaussagen gezeigt werden. Danach leiten wir verschiedene Beziehungen zwischen den Bildmengen, bzw., zwischen den Mengen der maximalen Elemente dieser Bildmengen der sechs Dualaufgaben her. Dazu zeigen wir unter welchen Bedingungen werden diese Mengen identisch. Ein allgemeines Schema das die Beziehungen zwischen den sechs dualen Mehrzieloptimierungsaufgaben und andere Dualaufgaben aus der Literatur enthält, wird dargestellt.

As the title already suggests the aim of the present work is to present Farkas - type results for inequality systems involving convex and/or non - convex functions. To be able to give the desired results, we treat optimization problems which involve convex and composed convex functions or non - convex functions like DC functions or fractions. To be able to use the fruitful Fenchel - Lagrange duality approach, to the primal problem we attach an equivalent problem which is a convex optimization problem. After giving a dual problem to the problem we initially treat, we provide weak necessary conditions which secure strong duality, i.e., the case when the optimal objective value of the primal problem coincides with the optimal objective value of the dual problem and, moreover, the dual problem has an optimal solution. Further, two ideas are followed. Firstly, using the weak and strong duality between the primal problem and the dual problem, we are able to give necessary and sufficient optimality conditions for the optimal solutions of the primal problem. Secondly, provided that no duality gap lies between the primal problem and its Fenchel - Lagrange - type dual we are able to demonstrate some Farkas - type results and thus to underline once more the connections between the theorems of the alternative and the theory of duality. One statement of the above mentioned Farkas - type results is characterized using only epigraphs of functions. We conclude our investigations by providing necessary and sufficient optimality conditions for a multiobjective programming problem involving composed convex functions. Using the well-known linear scalarization to the primal multiobjective program a family of scalar optimization problems is attached. Further to each of these scalar problems the Fenchel - Lagrange dual problem is determined. Making use of the weak and strong duality between the scalarized problem and its dual the desired optimality conditions are proved. Moreover, the way the dual problem of the scalarized problem looks like gives us an idea about how to construct a vector dual problem to the initial one. Further weak and strong vector duality assertions are provided.