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81	Bid Forecasting in Public Procurement / Budgivningsmodeller i offentliga upphandlingar Stiti, Karim, Yape, Shih Jung January 2019 (has links) Public procurement amounts to a significant part of Sweden's GDP. Nevertheless, it is an overlooked sector characterized by low digitization and inefficient competition where bids are not submitted based on proper mathematical tools. This Thesis seeks to create a structured approach to bidding in cleaning services by determining factors affecting the participation and pricing decision of potential buyers. Furthermore, we assess price prediction by comparing multiple linear regression models (MLR) to support vector regression (SVR). In line with previous research in the construction sector, we find significance for several factors such as project duration, location and type of contract on the participation decision in the cleaning sector. One notable deviant is that we do not find contract size to have an impact on the pricing decision. Surprisingly, the performance of MLR are comparable to more advanced SVR models. Stochastic dominance tests on price performance concludes that experienced bidders perform better than their inexperienced counterparts and companies place more competitive bids in lowest price tenders compared to economically most advantageous tenders (EMAT) indicating that EMAT tenders are regarded as unstructured. However, no significance is found for larger actors performing better in bidding than smaller companies. / Offentliga upphandlingar utgör en signifikant del av Sveriges BNP. Trots detta är det en förbisedd sektor som karakteriseras av låg digitalisering och ineffektiv konkurrens där bud läggs baserat på intuition snarare än matematiska modeller. Denna avhandling ämnar skapa ett strukturerat tillvägagångssätt för budgivning inom städsektorn genom att bestämma faktorer som påverkar deltagande och prissättning. Vidare undersöker vi prisprediktionsmodeller genom att jämföra multipel linjära regressionsmodeller med en maskininlärningsmetod benämnd support vector regression. I enlighet med tidigare forskning i byggindustrin finner vi att flera faktorer som typ av kontrakt, projekttid och kontraktsplats har en statistisk signifikant påverkan på deltagande i kontrakt i städindustrin. En anmärkningsvärd skillnad är att kontraktsvärdet inte påverkar prissättning som tidigare forskning visat i andra områden. För prisprediktionen är det överraskande att den enklare linjära regressionsmodellen presterar jämlikt till den mer avancerade maskininlärningsmodellen. Stokastisk dominanstest visar att erfarna företag har en bättre precision i sin budgivning än mindre erfarna företag. Därtill lägger företag överlag mer konkurrenskraftiga bud i kontrakt där kvalitetsaspekter tas i beaktning utöver priset. Vilket kan indikera att budgivare upplever dessa kontrakt som mindre strukturerade. Däremot finner vi ingen signifikant skillnad mellan större och mindre företag i denna bemärkning. Bidding in public procurement Count data regression Economically most advantageous tenders Lowest price tenders Machine learning Multiple linear regression Nonparametric bootstrap Position performance coefficient Sealed-bid auctions Stochastic dominance Support vector regression. Ekonomiskt mest fördelaktiga anbud Förseglade auktioner Lägsta-pris anbud Maskininlärning Multipel linjär regression. Engineering and Technology Teknik och teknologier
82	Application of the Duality Theory Lorenz, Nicole 15 August 2012 (has links) (PDF) The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem. Konjugierte Dualität konvexe Analysis Fencheldualität Lagrangedualität Regularitätsbedingungen schwache Dualität starke Dualität Portfoliooptimierung innere Punktbedingungen Regularitätsbedingungen Risikomaße Support Vektor Regression Suport Vektor Klassifikation Machinelles Lernen Conjugate duality convex duality theory Fenchel duality Lagrange duality Fenchel-Lagrange duality regularity conditions perturbation functions composed convex optimization problems geometric constraints cone constraints weak and strong duality scalar optimization interior point regularity condition conjugate functions convex risk measures convex deviation measures portfolio optimization optimality conditions stochastic programming chance constraints machine learning Tikhonov regularization loss functions Support Vector Regression Support Vector Classification concrete compressive strength ddc:515 Maschinelles Lernen Konjugierte Dualität konvexe Analysis
83	Application of the Duality Theory: New Possibilities within the Theory of Risk Measures, Portfolio Optimization and Machine Learning Lorenz, Nicole 28 June 2012 (has links) The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem. info:eu-repo/classification/ddc/515 ddc:515

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