In this dissertation we first consider a parallel linear model with correlated dual responses on a symmetric compact design region and construct locally optimal designs for estimating the location-shift parameter. These locally optimal designs are variant under linear transformation of the design space and depend on the correlation between the dual responses in an interesting and sensitive way. Subsequently, minimax and maximin efficient designs for estimating the location-shift parameter are derived. A comparison of the behavior of efficiencies between the minimax and maximin efficient designs relative to locally optimal designs is also provided. Both minimax or maximin efficient designs have advantage in terms of estimating efficiencies in different situations. Thirdly, we consider a linear regression model with a one-dimensional control variable x and an m-dimensional response variable y=(y_1,...,y_m). The components of y are correlated with a known covariance matrix. The calibration problem discussed here is based on the assumed regression model. It is of interest to obtain a suitable estimation of the corresponding x for a given target T=(T_1,...,T_m) on the expected responses. Due to the fact that there is more than one target value to be achieved in the multiresponse case, the m expected responses may meet their target values at different respective control values. Consideration includes the deviation of the expected response E(y_i) from its corresponding target value T_i for each component and the optimal value of calibration point x, say x_0, is considered to be the one which minimizes the weighted sum of squares of such deviations within the range of x. The objective of this study is to find a locally optimal design for estimating x_0, which minimizes the mean square error of the difference between x_0 and its estimator. It shows the optimality criterion is approximately equivalent to a c-criterion under certain conditions and explicit solutions with dual responses under linear and quadratic polynomial regressions are obtained.

This dissertation was to study computational theory and methods for ?nding multiple saddle critical points in Banach spaces. Two local minimax methods were developed for this purpose. One was for unconstrained cases and the other was for constrained cases. First, two local minmax characterization of saddle critical points in Banach spaces were established. Based on these two local minmax characterizations, two local minimax algorithms were designed. Their ?ow charts were presented. Then convergence analysis of the algorithms were carried out. Under certain assumptions, a subsequence convergence and a point-to-set convergence were obtained. Furthermore, a relation between the convergence rates of the functional value sequence and corresponding gradient sequence was derived. Techniques to implement the algorithms were discussed. In numerical experiments, those techniques have been successfully implemented to solve for multiple solutions of several quasilinear elliptic boundary value problems and multiple eigenpairs of the well known nonlinear p-Laplacian operator. Numerical solutions were presented by their pro?les for visualization. Several interesting phenomena of the solutions of quasilinear elliptic boundary value problems and the eigenpairs of the p-Laplacian operator have been observed and are open for further investigation. As a generalization of the above results, nonsmooth critical points were considered for locally Lipschitz continuous functionals. A local minmax characterization of nonsmooth saddle critical points was also established. To establish its version in Banach spaces, a new notion, pseudo-generalized-gradient has to be introduced. Based on the characterization, a local minimax algorithm for ?nding multiple nonsmooth saddle critical points was proposed for further study.

Les théories du choix social et de la décision multicritère sont fertiles en résultats paradoxaux. C'est à l'étude de quelques-uns d'entre eux qu'est consacrée cette thèse. Nous montrons tout d'abord les liens étroits entre ces deux domaines de recherche. Nous passons alors en revue les principaux paradoxes rencontrés dans ces deux domaines et tentons de classifier les méthodes utilisées pour les expliquer. Nous nous attaquons à notre tour à quatre types de paradoxes. L'étude des restrictions imposées par certaines conditions de transitivité de la méthode majoritaire donne des résultats surprenants. Nous les analysons en introduisant la notion de polydiversité. La règle de prudence (minimax) ne respecte pas l'axiome de cohérence. De plus, les vainqueurs prudents peuvent aussi être des vaincus prudents. Ces paradoxes liés à la prudence sont étudiés théoriquement, en particulier en utilisant la représentation géométrique des profils, et expérimentalement à l'aide de simulations. Pour certaines méthodes, l'amélioration de la position d'un candidat dans la préférence d'un votant peut conduire à une dégradation de sa situation du point de vue de la société. Nous analysons ce paradoxe en détail, en particulier pour les méthodes de rangement construites en itérant une fonction de choix. Nous terminons en étudiant la sensibilité de la méthode prudente et de la méthode de Borda à une variation du poids des critères. La comparaison des valeurs des indicateurs proposés donne des résultats inattendus.

Les données du monde réel sont souvent de très grande dimension, faisant intervenir un grand nombre de variables non pertinentes ou redondantes. La sélection de variables est donc utile dans ce cadre. D'abord, on considère la sélection de variables dans le modèle de régression quand le nombre de variables est très grand. En particulier on traite le cas où le nombre de variables pertinentes est bien plus petit que la dimension ambiante. Sans supposer aucune forme paramétrique pour la fonction de régression, on obtient des conditions minimales permettant de retrouver l'ensemble des variables pertinentes. Ces conditions relient la dimension intrinsèque à la dimension ambiante et la taille de l'échantillon. Ensuite, on considère le problème du test d'une hypothèse nulle composite sous un modèle de régression non paramétrique multi varié. Pour une fonctionnelle quadratique donnée $Q$, l'hypothèse nulle correspond au fait que la fonction $f$ satisfait la contrainte $Q[f] = 0$, tandis que l'alternative correspond aux fonctions pour lesquelles $ |Q[f]|$ est minorée par une constante strictement positive. On fournit des taux minimax de test et les constantes de séparation exactes ainsi qu'une procédure optimale exacte, pour des fonctionnelles quadratiques diagonales et positives. On peut utiliser ces résultats pour tester la pertinence d'une ou plusieurs variables explicatives. L'étude des taux minimax pour les fonctionnelles quadratiques diagonales qui ne sont ni positives ni négatives, fait apparaître deux régimes différents : un régime " régulier " et un régime " irrégulier ". On applique ceci au test de l'égalité des normes de deux fonctions observées dans des environnements bruités

This thesis investigates several design problems concerning two-channel conjugate quadrature (CQ) filter banks and orthogonal wavelets, as well as orthogonal cosine-modulated (OCM) filter banks. It is well known that optimal design of CQ filters and wavelets and optimal design of prototype filters (PFs) of OCM filter banks in the least squares (LS) or minimax sense are nonconvex problems and to date only local solutions can be claimed. In this thesis, we first make some improvements over several direct design techniques for local design problems in terms of convergence and solution accuracy. By virtue of the recent progress in global polynomial optimization and the improved local design methods mentioned above, we describe an attempt at developing several design strategies that may be viewed as our endeavors towards global solutions for LS CQ filter banks, minimax CQ filter banks, and OCM filter banks. In brief terms, the proposed design strategies are based on several observations made among globally optimal impulse responses of low-order filter banks, and are essentially order-recursive algorithms in terms of filter length combined with some techniques in identifying a desirable initial point in each round of iteration. This main idea is applied to three design scenarios in this thesis, namely, LS design of orthogonal filter banks and wavelets, minimax design of orthogonal filter banks and wavelets, and design of orthogonal cosine-modulated filter banks. Simulation studies are presented to evaluate and compare the performance of the proposed design methods with several well established algorithms in the literature.

建立指數基金時，通常是利用追蹤指數的技巧，選取少量的股票建構指數基金使得報酬率與標的指數(benchmark index)報酬率同步的投資組合。如果能建立包含少量股票的投資組合，就可達到指數追蹤的效果，那麼也能利用少量的股票建立績效可以超越指數基金的投資組合。本論文利用建構指數基金的方法以及大中取小的概念，挑選出一個績效可以超越標的指數的投資組合。本論文提出的模型亦考慮實務上交易所需的各項成本、整數交易單位與資產總類數等限制。因此，模型包含整數變數與二元變數。最後以台灣加權股價指數的相關資料做為實證研究的對象，實證結果顯示本論文提出的模型所建立的投資組合超越標的指數的績效平均年化報酬率25%。 / Setting up an index fund usually uses techniques of index-tracking that choosing few stocks forming a portfolio to obtain the same return rate as the benchmark index. Similarly we can use the same concept to set up a portfolio such that the performance is better than index’s. In this thesis we use index-tracking methods and minimax rule to obtain a portfolio which outperforms the benchmark index. In the proposed mathematical model we will consider the transaction costs, integer trading unit volume, and the total number of assets in the portfolio. Therefore the resulting model is a mixed integer nonlinear programming including integer variables and binary variables. Finally, the empirical study will be performed by using the data from the Taiwan stock market to verify the performance of our model. The empirical study shows that the portfolios created by our models outperform the benchmark index up to 25% in average.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-17T17:56:04Z No. of bitstreams: 1 JEFFERSON ABRANTES DOS SANTOS - DISSERTAÇÃO PPGMAT 2007..pdf: 851615 bytes, checksum: 3c65fe64e44e2b25e61689585f18f5bb (MD5) / Made available in DSpace on 2018-07-17T17:56:05Z (GMT). No. of bitstreams: 1 JEFFERSON ABRANTES DOS SANTOS - DISSERTAÇÃO PPGMAT 2007..pdf: 851615 bytes, checksum: 3c65fe64e44e2b25e61689585f18f5bb (MD5) Previous issue date: 2007-12 / CNPq / Capes / Neste trabalho estudamos a existência de solução não nula, via Métodos Variacionais para uma classe de problemas Elípticos onde f :R→R apresenta uma descontinuidade, do tipo salto, com seu conjunto de pontos de descontinuidade sendo um conjunto enumerável sem pontos de acumulação e Ω é um domínio limitado com fronteira suave. * Para Visualisar as equações ou formulas originalmente escritas neste resumo recomendamos o downloado do arquivo completo. / In this work we study the existence of solutions for the following class of Elliptic problems wherethefunctionf :R →RhassomediscontinuitiesandΩisaboundeddomainwith smooth boundary. The main tool used is the Variational Methods together arguments developed by Chang [9]. *To see the equations or formulas originally written in this summary we recommend downloading the complete file.

Le travail dans cette thèse porte sur le problème de détection «one among many» où l’on doit distinguer entre un bruit sous H0 et une parmi L alternatives connues sous H1. Ce travail se concentre sur l’étude et la mise en œuvre de méthodes de détection robustes de dimension réduite utilisant des dictionnaires optimisés. Ces méthodes de détection sont associées au test de Rapport de Vraisemblance Généralisé. Les approches proposées sont principalement évaluées sur des données hyperspectrales. Dans la première partie, plusieurs sujets techniques associés à cette thèse sont présentés. La deuxième partie met en évidence les aspects théoriques et algorithmiques des méthodes proposées. Deux inconvénients liés à un grand nombre d’alternatives se posent. Dans ce cadre, nous proposons des techniques d’apprentissage de dictionnaire basées sur un critère robuste qui cherche à minimiser la perte de puissance dans le pire des cas (type minimax). Dans le cas où l’on cherche un dictionnaire à K = 1 atome, nous montrons que la solution exacte peut être obtenue. Ensuite, nous proposons dans le cas K > 1 trois algorithmes d’apprentissage minimax. Finalement, la troisième partie de ce manuscrit présente plusieurs applications. L’application principale concerne les données astrophysiques hyperspectrales de l’instrument Multi Unit Spectroscopic Explorer. Les résultats numériques montrent que les méthodes proposées sont robustes et que le cas K > 1 permet d’augmenter les performances de détection minimax par rapport au cas K = 1. D’autres applications possibles telles que l’apprentissage minimax de visages et la reconnaissance de chiffres manuscrits dans le pire cas sont présentées. / This Ph.D dissertation deals with a "one among many" detection problem, where one has to discriminate between pure noise under H0 and one among L known alternatives under H1. This work focuses on the study and implementation of robust reduced dimension detection tests using optimized dictionaries. These detection methods are associated with the Generalized Likelihood Ratio test. The proposed approaches are principally assessed on hyperspectral data. In the first part, several technical topics associated to the framework of this dissertation are presented. The second part highlights the theoretical and algorithmic aspects of the proposed methods. Two issues linked to the large number of alternatives arise in this framework. In this context, we propose dictionary learning techniques based on a robust criterion that seeks to minimize the maximum power loss (type minimax). In the case where the learned dictionary has K = 1 column, we show that the exact solution can be obtained. Then, we propose in the case K > 1 three minimax learning algorithms. Finally, the third part of this manuscript presents several applications. The principal application regards astrophysical hyperspectral data of the Multi Unit Spectroscopic Explorer instrument. Numerical results show that the proposed algorithms are robust and in the case K > 1 they allow to increase the minimax detection performances over the K = 1 case. Other possible applications such as worst-case recognition of faces and handwritten digits are presented.

This work deals with design and construction of a robotics checkers player based on computer vision, a move solving algorithm Minimax and a industrial manipulator EPSON C3. Work also deals with design of robot communication protocol and C# communication library execution.

Over the past decades, cost-effectiveness principle or cost-benefit analysis has been employed oftentimes as a typical assessment tool for the expansion of drinking water utility. With changing public awareness of the inherent linkages between climate change, population growth and economic development, the addition of global change impact in the assessment regime has altered the landscape of traditional evaluation matrix. Nowadays, urban drinking water infrastructure requires careful long-term expansion planning to reduce the risk from global change impact with respect to greenhouse gas (GHG) emissions, economic boom and recession, as well as water demand variation associated with population growth and migration. Meanwhile, accurate prediction of municipal water demand is critically important to water utility in a fast growing urban region for the purpose of drinking water system planning, design and water utility asset management. A system analysis under global change impact due to the population dynamics, water resources conservation, and environmental management policies should be carried out to search for sustainable solutions temporally and spatially with different scales under uncertainties. This study is aimed to develop an innovative, interdisciplinary, and insightful modeling framework to deal with global change issues as a whole based on a real-world drinking water infrastructure system expansion program in Manatee County, Florida. Four intertwined components within the drinking water infrastructure system planning were investigated and integrated, which consists of water demand analysis, GHG emission potential, system optimization for infrastructure expansion, and nested minimax-regret (NMMR) decision analysis under uncertainties. In the water demand analysis, a new system dynamics model was developed to reflect the intrinsic relationship between water demand and changing socioeconomic iv environment. This system dynamics model is based on a coupled modeling structure that takes the interactions among economic and social dimensions into account offering a satisfactory platform. In the evaluation of GHG emission potential, a life cycle assessment (LCA) is conducted to estimate the carbon footprint for all expansion alternatives for water supply. The result of this LCA study provides an extra dimension for decision makers to extract more effective adaptation strategies. Both water demand forecasting and GHG emission potential were deemed as the input information for system optimization when all alternatives are taken into account simultaneously. In the system optimization for infrastructure expansion, a multiobjective optimization model was formulated for providing the multitemporal optimal facility expansion strategies. With the aid of a multi-stage planning methodology over the partitioned time horizon, such a systems analysis has resulted in a full-scale screening and sequencing with respect to multiple competing objectives across a suite of management strategies. In the decision analysis under uncertainty, such a system optimization model was further developed as a unique NMMR programming model due to the uncertainties imposed by the real-world problem. The proposed NMMR algorithm was successfully applied for solving the real-world problem with a limited scale for the purpose of demonstration.