It is frequently the case that deterministic optimization models could be made more practical by explicitly incorporating uncertainty. The resulting stochastic optimization problems are in general more difficult to solve than their deterministic counterparts, because the objective function cannot be evaluated exactly and/or because there is no explicit relation between the objective function and the corresponding decision variables. This thesis develops random search algorithms for solving optimization problems with continuous decision variables when the objective function values can be estimated with some noise via simulation. Our algorithms will maintain a set of sampled solutions, and use simulation results at these solutions to guide the search for better solutions. In the first part of the thesis, we propose an Adaptive Search with Resampling and Discarding (ASRD) approach for solving continuous stochastic optimization problems. Our ASRD approach is a framework for designing provably convergent algorithms that are adaptive both in seeking new solutions and in keeping or discarding already sampled solutions. The framework is an improvement over the Adaptive Search with Resampling (ASR) method of Andradottir and Prudius in that it spends less effort on inferior solutions (the ASR method does not discard already sampled solutions). We present conditions under which the ASRD method is convergent almost surely and carry out numerical studies aimed at comparing the algorithms. Moreover, we show that whether it is beneficial to resample or not depends on the problem, and analyze when resampling is desirable. Our numerical results show that the ASRD approach makes substantial improvements on ASR, especially for difficult problems with large numbers of local optima. In traditional simulation optimization problems, noise is only involved in the objective functions. However, many real world problems involve stochastic constraints. Such problems are more difficult to solve because of the added uncertainty about feasibility. The second part of the thesis presents an Adaptive Search with Discarding and Penalization (ASDP) method for solving continuous simulation optimization problems involving stochastic constraints. Rather than addressing feasibility separately, ASDP utilizes the penalty function method from deterministic optimization to convert the original problem into a series of simulation optimization problems without stochastic constraints. We present conditions under which the ASDP algorithm converges almost surely from inside the feasible region, and under which it converges to the optimal solution but without feasibility guarantee. We also conduct numerical studies aimed at assessing the efficiency and tradeoff under the two different convergence modes. Finally, in the third part of the thesis, we propose a random search method named Gaussian Search with Resampling and Discarding (GSRD) for solving simulation optimization problems with continuous decision spaces. The method combines the ASRD framework with a sampling distribution based on a Gaussian process that not only utilizes the current best estimate of the optimal solution but also learns from past sampled solutions and their objective function observations. We prove that our GSRD algorithm converges almost surely, and carry out numerical studies aimed at studying the effects of utilizing the Gaussian sampling strategy. Our numerical results show that the GSRD framework performs well when the underlying objective function is multi-modal. However, it takes much longer to sample solutions, especially in higher dimensions.

Triggered by the negative economic and social consequences of the 2008/09 global financial crisis, critical questions about how financial markets operate and how they benefit society have received renewed attention. In response to these questions, new investment strategies whose objectives go beyond pure financial return have emerged. Impact investing, a concept which closely co-exists with investment strategies such as socially responsible investing and responsible investing, is the latest attempt to combine financial return with a contribution to the sustainable development of society. Although still in the early days of its development, impact investing is a maturing field to the extent that it has developed into a global phenomenon with an emerging global support structure. While impact investing still occupies a tiny niche in South Africa's investment market, there is, at least compared to other developing countries on the African continent, a large community of South African impact investors who are looking to invest locally and beyond. This research investigates how far the understanding and practice of impact investing in South Africa is influenced by global efforts to build the field and to what extent context specific factors are shaping the way in which it is currently evolving. In other words, how both global convergence and local divergence mechanisms interplay to form what is the South African impact investing market. The research findings suggest that while the international movement towards the standardisation of impact investing practices has reached South Africa, context specific factors such as, among others, the social, racial and political legacy of apartheid and the existence of a sophisticated financial system are central to the way in which the field is taking shape.

The international marketing literature has a common assumption that consumers across countries are becoming more similar in their consumption behavior over time. However, this assumption of global convergence of consumer spending has not been empirically tested in the literature. In this dissertation, we examine the convergence hypothesis across a heterogeneous set of countries and multiple product categories. In the first essay, we develop a conceptual framework of convergence of consumer spending behavior. In the second essay, we empirically test whether convergence is observed across markets and product categories over time. Finally, in the third essay, we investigate the effect of global convergence of consumer spending on market concentration and firms’ market shares. Using the four-firm concentration ratio, we compute the market concentration by industry in each market to investigate the effect of convergence on market concentration. We also examine the effect of convergence on market shares of individual firms, considering the moderating effects of country of origin, country of operation, and the degree of internationalization of the firm. We model the dependent variables, market concentration and market shares, using the fractional logit model. Our results show that there is an overall convergence trend across product categories and countries over time. Moreover, we find that convergence increases the market shares of the largest firms in a market. The findings of this study have theoretical and managerial implications on major marketing areas including global marketing strategy, internationalization, and market segmentation.

Mathematical program with equilibrium constraints (MPEC)has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC.A primal-dual interior point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or linear independence constraint qualification. Under very general assumptions, the algorithm can always find some point with strong or weak stationarity. In particular, it is shown that every limiting point of the generated sequence is a piece-wise stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a certain point with weak stationarity can be obtained. Preliminary numerical results are satisfactory, which include a case analyzed by Leyffer for which the penalty interior point algorithm failed to find a stationary solution. / Singapore-MIT Alliance (SMA)

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第17968号 / 情博第512号 / 新制||情||91(附属図書館) / 30798 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 中村 佳正, 教授 西村 直志, 准教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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Orientadores: Sandra Augusta Santos, Márcia Aparecida Gomes-Ruggiero / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T21:37:45Z (GMT). No. of bitstreams: 1 Sachine_Mael_D.pdf: 4721541 bytes, checksum: 0506c48fbbc3961c4626c36a0487fa1c (MD5) Previous issue date: 2010 / Resumo: Neste trabalho propomos modificações globalmente convergentes para o Método das Assíntotas Móveis (MMA), baseadas no parâmetro espectral para a construção das aproximações das funções originais e na relaxação da condição conservadora. A informação de segunda ordem presente no parâmetro espectral é incluída nas aproximações racionais da função objetivo e das restrições não-lineares no início de cada iteração, de modo a melhorar a qualidade dos modelos. A condição conservadora é relaxada por meio de uma seqüência forçante controlada somável, de maneira que a convergência global é mantida. Também, propomos uma nova estratégia para resolver os subproblemas MMA por meio do problema dual, usando uma técnica de região de confiança. Os experimentos numéricos realizados comprovam a eficiência das estratégias propostas. Ainda, por trabalharmos com um problema aumentado associado à formulação padrão para o problema de programação não-linear com restrições de desigualdade, estabelecemos relações entre os pontos KKT do problema aumentado e os pontos correspondentes do problema original associado / Abstract: In this work we propose globally convergent versions for the Method of Moving Asymptotes (MMA), based on the spectral parameter for updating the approximations of the original functions and on relaxing the conservative condition. The second-order information present in the spectral parameter is included in the rational approximations of the objective function and of the nonlinear constraints in the beginning of each iteration, so as to improve the quality of the models. The conservative condition is relaxed by means of a summable controlled forcing sequence, so that global convergence is maintained. Also, we propose a new strategy to solve the MMA subproblems by means of the dual problem, using a trust-region technique. The performed numerical experiments confirm the efficiency of the proposed strategies. In addition, by working with an extended problem associated with the standard formulation for the nonlinear programming problem with inequality constraints, we have established relationships between the KKT points of the extended problem and the corresponding points of the associated original problem / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19122号 / 情博第568号 / 新制||情||100(附属図書館) / 32073 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 山下 信雄, 教授 太田 快人, 教授 永持 仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Les problèmes de complémentarité interviennent dans de nombreux domaines scientifiques : économie, mécanique des solides, mécanique des fluides. Ce n’est que récemment qu’ils ont commencé d’intéresser les chercheurs étudiant les écoulements et le transport en milieu poreux. Les problèmes de complémentarité sont un cas particulier des inéquations variationnelles. Dans cette thèse, on offre plusieurs contributions aux méthodes numériques pour résoudre les problèmes de complémentarité. Dans la première partie de cette thèse, on étudie les problèmes de complémentarité linéaires 0 6 x ⊥ (Mx+q) > 0 où, x l’inconnue est dans Rn et où les données sont q, un vecteur de Rn, et M, une matrice d’ordre n. L’existence et l’unicité de ce problème est obtenue quand la matrice M est une P-matrice. Une méthode très efficace pour résoudre les problèmes de complémentarité est la méthode de Newton-min, une extension de la méthode de Newton aux problèmes non lisses.Dans cette thèse on montre d’abord, en construisant deux familles de contre-exemples, que la méthode de Newton-min ne converge pas pour la classe des P-matrices, sauf si n= 1 ou 2. Ensuite on caractérise algorithmiquement la classe des P-matrices : c’est la classe des matrices qui sont telles que quel que, soit le vecteur q, l’algorithme de Newton-min ne fait pas de cycle de deux points. Enfin ces résultats de non-convergence nous ont conduit à construire une méthode de globalisation de l’algorithme de Newton-min dont nous avons démontré la convergence globale pour les P-matrices. Des résultats numériques montrent l’efficacité de cet algorithme et sa convergence polynomiale pour les cas considérés. Dans la deuxième partie de cette thèse, nous nous sommes intéressés à un exemple de problème de complémentarité non linéaire concernant les écoulements en milieu poreux. Il s’agit d’un écoulement liquide-gaz à deux composants eau-hydrogène que l’on rencontre dans le cadre de l’étude du stockage des déchets radioactifs en milieu géologique. Nous présentons un modèle mathématique utilisant des conditions de complémentarité non linéaires décrivant ces écoulements. D’une part, nous proposons une méthode de résolution et un solveur pour ce problème. D’autre part, nous présentons les résultats numériques que nous avons obtenus suite à la simulation des cas-tests proposés par l’ANDRA (Agence Nationale pour la gestion des Déchets Radioactifs) et le GNR MoMaS. En particulier, ces résultats montrent l’efficacité de l’algorithme proposé et sa convergence quadratique pour ces cas-tests / This manuscript deals with numerical methods for linear and nonlinear complementarity problems,and, more specifically, with solving gas phase appearance and disappearance modeled as a complementarity problem. In the first part of this manuscript, we focused on the plain Newton-min method to solve the linear complementarity problem (LCP for short) 0 6 x ⊥ (Mx+q) > 0 that can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x,Mx+q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm was known to converge in at most n iterations. We show that this resultno longer holds when M is a P-matrix of order > 3. On the one hand, we offer counter-examplesshowing that the algorithm may cycle in those cases. P-matrices are interesting since they are thoseensuring the existence and uniqueness of the solution to the LCP for an arbitrary q. Incidentally,convergence occurs for a P-matrix of order 1 or 2. On the other hand, we provide a new algorithmic characterization of P-matricity : we show that a nondegenerate square real matrix M is a P-matrixif and only if, whatever is the real vector q, the Newton-min algorithm does not cycle between twopoints. In order to force the convergence of the Newton-min algorithm with P-matrices, we havederived a new method, which is robust, easy to describe, and simple to implement. It is globallyconvergent and the numerical results reported in this manuscript show that it outperforms a methodof Harker and Pang. In the second part of this manuscript, we consider the modeling of migration of hydrogen produced by the corrosion of the nuclear waste packages in an underground storage including the dissolution of hydrogen. It results in a set of nonlinear partial differential equations with nonlinear complementarity constraints. We show how to apply a robust and efficient solution strategy, the Newton-min method considered for LCP in the first part, to this geoscience problem and investigates its applicability and efficiency on this difficult problem. The practical interest of this solution technique is corroborated by numerical experiments from the Couplex Gas benchmark proposed by Andra and GNR MoMas. In particular, numerical results show that the Newton-min method is quadratically convergent for these problems

L'hadronthérapie est une modalité d'irradiation récente particulièrement attractive. Les ions, par leur profil caractéristique de dépôt de dose dans la matière et leur efficacité biologique accrue, sont des particules parfaitement adaptées pour le traitement du cancer. C’est une modalité émergente et les travaux de recherche et de développement qui en font l'objet se poursuivent de manière soutenue. Cependant, il n'existe à ce jour aucun outil permettant de quantifier pour le patient le gain clinique associé aux améliorations proposées, comme l’apport d’une gantry par exemple. Nous proposons dans ce travail de concevoir un module de planification inverse du traitement pour un but prospectif. Détachée des contraintes usuelles de précision et de temps de calcul, notre méthode d'optimisation se base sur un algorithme génétique afin d'approcher d'une solution globale vis-à-vis d'un grand nombre de paramètres balistiques (champs d’irradiation libres) et en associant les diverses régions d'intérêt dosimétrique. La stratégie d'optimisation retenue est progressivement complexifiée afin de prendre en compte de manière efficace les différents enjeux de la planification. La robustesse du plan vis-à-vis des incertitudes inhérentes au traitement, primordiale en hadronthérapie, est évaluée. Dans toutes les situations testées, il apparaît que l'inclusion dans l'optimisation de paramètres habituellement fixés manuellement permet une amélioration de la qualité de traitement. Nous proposons au terme de cette étude un outil prospectif d'optimisation au réglage simple et capable de mener des études comparées sur la pertinence de nouvelles modalités d’irradiation. / Hadrontherapy is a recent and particularly attractive modality. Characterized by a specific dose deposition profile in matter and by a high biological effectiveness, ions are found to be very well-suited for cancer treatment. As an emergent modality, the research in hadrontherapy is extremely active and promises many improvements for the future. However, there is no tool to date to quantify the clinical benefit for the patient related to the proposed improvements, the use of a gantry for example. In this work, we propose to use the treatment planning system, usually dedicated to clinical practice, in a prospective purpose. Suppressing the classical constraints of precision and time, our optimization method is based on a genetic algorithm designed to approach a global solution including a high number of balistic parameters (free irradiation fields) for all regions of dosimetric interest. The optimization strategy is progressively complicated in order to efficientely take into account the main issues of the inverse planning problem. The robustness of plans towards the uncertainties related to the application of the treatment, essential in hadrontherapy, is evaluated. The results show that the inclusion, in the optimization, of parameters usually fixed by the human planner leads systematically to an improved treatment quality. The final product of this work is a prospective optimization tool characterized by an easy set-up system and the ability to perform comparative studies on the relevance of new irradiation modalities.