O método do Gradiente Espectral, introduzido por Barzilai e Borwein e analisado por Raydan, para minimização irrestrita, é um método simples cujo desempenho é comparável ao de métodos tradicionais como, por exemplo, gradientes conjugados. Desde a introdução do método, assim como da sua extensão para minimização em conjuntos convexos, foram introduzidas várias combinações de passos espectrais diferentes, assim como de buscas lineares não monótonas diferentes. Dos resultados numéricos apresentados em vários trabalhos não é possível inferir se existem diferenças significativas no desempenho dos diversos métodos. Além disso, também não fica clara a relevância das buscas não monótonas como uma ferramenta em si próprias ou se, na verdade, elas são úteis apenas para permitir que o método seja o mais parecido possível com o método original de Barzilai e Borwein. O objetivo deste trabalho é comparar os diversos métodos recentemente introduzidos como combinações de diferentes buscas lineares não monótonas e diferentes passos espectrais para encontrar a melhor combinação e, a partir daí, aferir o desempenho numérico do método. / The Spectral Gradient method, introduced by Barzilai and Borwein and analized by Raydan for unconstrained minimization, is a simple method whose performance is comparable to traditional methods, such as conjugate gradients. Since the introduction of method, as well as its extension to minimization of convex sets, there were introduced various combinations of different spectral steplengths, as well as different nonmonotone line searches. By the numerical results presented in many studies it is not possible to infer whether there are siginificant differences in the performance of various methods. It also is not sure the relevance of the nonmonotone line searches as a tool in themselves or whether, in fact, they are usefull only to allow the method to be as similar as possible with the original method of Barzilai e Borwein. The objective of this study is to compare the different methods recently introduced as different combinations of nonmonotone linear searches and different spectral steplengths to find the best combination and from there, evaluating the numerical performance of the method.

Despite its simple construction, robustness and low manufacturing cost, the application areas of SR motors are remained limited due to the high level of acoustic noise and torque ripple. In this thesis work, two different type of controllers are designed and implemented in order to minimize the acoustic noise and torque ripple which are considered as the major problems of SR motors. In this scope, first the possible acoustic noise sources are investigated. A sliding mode controller is designed and implemented to reduce the shaft torque ripple which is considered as a major source of acoustic noise. The performance of the controller is experimentally tested and it is observed that especially in low speed region reduction of torque ripple is significant. The torque ripple minimization performance of the controller is also tested at different speeds and the acoustic noise levels are recorded simultaneously. Comparing the noise mitigation with the noise reduction the correlation between the acoustic noise and shaft torque ripple is investigated. The results obtained from this investigation indicated that the torque ripple is not a major source of acoustic noise in SR motors. After this finding, radial force which is the other possible acoustic noise source of SRM is taken into consideration. The effects of control parameters on radial force and the motor efficiency are investigated via simulations. With the intuition obtained from this analysis, a switching angle neuro-controller is designed to minimize the peak level of radial forces. The performance of the mentioned controller is verified through noise records under steady state conditions. Regarding to the radial force simulations and the acoustic noise measurements, it is deduced that the radial force is the major source of acoustic noise. On the other hand, another controller is designed and implemented which increases the average torque per ampere value in order to increase the efficiency of the motor. It is seen that this controller has a good effect on increasing the efficiency but does not guarantee to operate at maximum efficiency.

published_or_final_version / Public Administration / Master / Master of Public Administration

A água é uma matéria-prima estratégica na indústria química, petroquímica e de alimentos, sendo utilizada em diversas etapas dos processos. Devido à importância econômica e ao impacto ambiental resultante do consumo da água na indústria, o uso racional da água vem sendo amplamente enfatizado. Nas últimas décadas, diversas metodologias foram propostas para a minimização do consumo de água e emissão de efluentes líquidos na indústria, baseadas em conceitos de integração mássica como reuso, reciclo e regeneração das correntes que conectam os processos. As metodologias propostas na literatura para a integração mássica dividem-se em dois grandes grupos: o primeiro utiliza a abordagem termodinâmica-heurística-evolutiva, enquanto que o segundo faz uso da programação matemática e otimização. Ambas as metodologias apresentam dificuldades para tratar do caso de múltiplos poluentes, sendo que na primeira, é necessário uma série de aproximações para tratar deste tipo de problema e na segunda estão presentes limitações relativas aos métodos de otimização. Além disso, sistemas integrados massicamente podem apresentar dificuldades operacionais devido ao maior número de reciclos e reusos de correntes. O presente trabalho através do uso de ferramentas de programação matemática e, baseado no problema padrão de síntese de redes proposto por Fontana (2002), propõe métodos para a redução da complexidade do problema de síntese e obtenção de redes integradas massicamente, considerando aspectos econômicos e operacionais. Inicialmente foi proposta a eliminação de variáveis inteiras do problema de otimização, transformando o problema de programação nãolinear inteira-mista (MINLP) em um problema de programação não-linear (NLP). Em seguida, foi proposta uma metodologia para a redução da complexidade do problema baseada na utilização das restrições de igualdade, reduzindo o número de variáveis de decisão. As formulações propostas apresentaram bons resultados, diminuindo consideravelmente o tempo computacional em relação ao problema MINLP original. Baseada nas metodologias desenvolvidas para redução da complexidade do problema, foi implementado ainda um gerador de estimativas iniciais viáveis utilizando números aleatórios. Também foram propostas três implementações para a síntese de redes com considerações econômicas e operacionais, resolvendo o problema de otimização em dois níveis: um externo para avaliação de critérios econômicos e um interno de onde é obtido o índice operacional. Das três formulações com considerações operacionais propostas, duas apresentaram redes com melhor desempenho operacional quando comparadas com os problemas somente com considerações econômicas. Tais resultados foram avaliados através de simulações dinâmicas com modelos linearizados, sendo observado, nestas duas implementações, aumento da robustez do sistema (redução da ação de controle sobre as variáveis manipuladas) frente a distúrbios positivos nas cargas de poluentes e mudanças nos set-points das variáveis controladas. / Water is an important raw material in the chemical, petrochemical, and food industry, being used in several stages of a process. Based on the economic importance of the water and the environmental impact through its employment in the industry, its rational consume has been receiving special attention. In the past decades, several methodologies have been proposed for the minimization of industrial water consume and wastewater emissions based on concepts of mass integration such as reuse, recycle, and regeneration of process streams. The methodologies proposed in the literature for the mass integration can be classified in two main groups: the first uses the themodynamic-heuristic-evolutive approach while the second uses mathematical programming and optimization. Both methodologies show difficulties to deal with the case of multiple pollutants: on the first one it is necessary to make some assumptions to solve this problem while the second, limitations relative to optimization methods are present. Another problem is the operational limitations due to streams recycle and reuse, that integrated processes can present. The present study, through the use of mathematical programming tools, based on the synthesis problem proposed by Fontana (2002), proposes methods to reduce the problem complexity and also for the synthesis of mass integration networks regarding economical and operational aspects. Initially it was proposed the elimination of the integer variables from the optimization problem, changing the problem from mixed-integer nonlinear programming (MINLP) to nonlinear programming (NLP). In the following, a methodology for the reduction of the problems complexity, based on the equality constraints, was applied to reduce the number of decision variables. The proposed formulations showed good results, reducing the computational time comparing to the MINLP problem. Based on the proposed methodologies for the reduction of the problem complexity described above, it was implemented a feasible initial guess generator based on random numbers. It was also proposed three formulations for the network synthesis with economic and operational considerations, solving the synthesis problem in two levels: an external level for the evaluation of economical criteria and an internal level where the operational index is obtained. Two out of the three implementations presented networks with better operational results comparing with problems only with economical aspects. These results were evaluated by dynamic simulations with linearized models and it was observed an increase in the systems robustness (reduction of the control action over the manipulated variables) when the system was subjected to positive disturbances in the pollutants loads and set-points changes.

A água é uma matéria-prima estratégica na indústria química, petroquímica e de alimentos, sendo utilizada em diversas etapas dos processos. Devido à importância econômica e ao impacto ambiental resultante do consumo da água na indústria, o uso racional da água vem sendo amplamente enfatizado. Nas últimas décadas, diversas metodologias foram propostas para a minimização do consumo de água e emissão de efluentes líquidos na indústria, baseadas em conceitos de integração mássica como reuso, reciclo e regeneração das correntes que conectam os processos. As metodologias propostas na literatura para a integração mássica dividem-se em dois grandes grupos: o primeiro utiliza a abordagem termodinâmica-heurística-evolutiva, enquanto que o segundo faz uso da programação matemática e otimização. Ambas as metodologias apresentam dificuldades para tratar do caso de múltiplos poluentes, sendo que na primeira, é necessário uma série de aproximações para tratar deste tipo de problema e na segunda estão presentes limitações relativas aos métodos de otimização. Além disso, sistemas integrados massicamente podem apresentar dificuldades operacionais devido ao maior número de reciclos e reusos de correntes. O presente trabalho através do uso de ferramentas de programação matemática e, baseado no problema padrão de síntese de redes proposto por Fontana (2002), propõe métodos para a redução da complexidade do problema de síntese e obtenção de redes integradas massicamente, considerando aspectos econômicos e operacionais. Inicialmente foi proposta a eliminação de variáveis inteiras do problema de otimização, transformando o problema de programação nãolinear inteira-mista (MINLP) em um problema de programação não-linear (NLP). Em seguida, foi proposta uma metodologia para a redução da complexidade do problema baseada na utilização das restrições de igualdade, reduzindo o número de variáveis de decisão. As formulações propostas apresentaram bons resultados, diminuindo consideravelmente o tempo computacional em relação ao problema MINLP original. Baseada nas metodologias desenvolvidas para redução da complexidade do problema, foi implementado ainda um gerador de estimativas iniciais viáveis utilizando números aleatórios. Também foram propostas três implementações para a síntese de redes com considerações econômicas e operacionais, resolvendo o problema de otimização em dois níveis: um externo para avaliação de critérios econômicos e um interno de onde é obtido o índice operacional. Das três formulações com considerações operacionais propostas, duas apresentaram redes com melhor desempenho operacional quando comparadas com os problemas somente com considerações econômicas. Tais resultados foram avaliados através de simulações dinâmicas com modelos linearizados, sendo observado, nestas duas implementações, aumento da robustez do sistema (redução da ação de controle sobre as variáveis manipuladas) frente a distúrbios positivos nas cargas de poluentes e mudanças nos set-points das variáveis controladas. / Water is an important raw material in the chemical, petrochemical, and food industry, being used in several stages of a process. Based on the economic importance of the water and the environmental impact through its employment in the industry, its rational consume has been receiving special attention. In the past decades, several methodologies have been proposed for the minimization of industrial water consume and wastewater emissions based on concepts of mass integration such as reuse, recycle, and regeneration of process streams. The methodologies proposed in the literature for the mass integration can be classified in two main groups: the first uses the themodynamic-heuristic-evolutive approach while the second uses mathematical programming and optimization. Both methodologies show difficulties to deal with the case of multiple pollutants: on the first one it is necessary to make some assumptions to solve this problem while the second, limitations relative to optimization methods are present. Another problem is the operational limitations due to streams recycle and reuse, that integrated processes can present. The present study, through the use of mathematical programming tools, based on the synthesis problem proposed by Fontana (2002), proposes methods to reduce the problem complexity and also for the synthesis of mass integration networks regarding economical and operational aspects. Initially it was proposed the elimination of the integer variables from the optimization problem, changing the problem from mixed-integer nonlinear programming (MINLP) to nonlinear programming (NLP). In the following, a methodology for the reduction of the problems complexity, based on the equality constraints, was applied to reduce the number of decision variables. The proposed formulations showed good results, reducing the computational time comparing to the MINLP problem. Based on the proposed methodologies for the reduction of the problem complexity described above, it was implemented a feasible initial guess generator based on random numbers. It was also proposed three formulations for the network synthesis with economic and operational considerations, solving the synthesis problem in two levels: an external level for the evaluation of economical criteria and an internal level where the operational index is obtained. Two out of the three implementations presented networks with better operational results comparing with problems only with economical aspects. These results were evaluated by dynamic simulations with linearized models and it was observed an increase in the systems robustness (reduction of the control action over the manipulated variables) when the system was subjected to positive disturbances in the pollutants loads and set-points changes.

A água é uma matéria-prima estratégica na indústria química, petroquímica e de alimentos, sendo utilizada em diversas etapas dos processos. Devido à importância econômica e ao impacto ambiental resultante do consumo da água na indústria, o uso racional da água vem sendo amplamente enfatizado. Nas últimas décadas, diversas metodologias foram propostas para a minimização do consumo de água e emissão de efluentes líquidos na indústria, baseadas em conceitos de integração mássica como reuso, reciclo e regeneração das correntes que conectam os processos. As metodologias propostas na literatura para a integração mássica dividem-se em dois grandes grupos: o primeiro utiliza a abordagem termodinâmica-heurística-evolutiva, enquanto que o segundo faz uso da programação matemática e otimização. Ambas as metodologias apresentam dificuldades para tratar do caso de múltiplos poluentes, sendo que na primeira, é necessário uma série de aproximações para tratar deste tipo de problema e na segunda estão presentes limitações relativas aos métodos de otimização. Além disso, sistemas integrados massicamente podem apresentar dificuldades operacionais devido ao maior número de reciclos e reusos de correntes. O presente trabalho através do uso de ferramentas de programação matemática e, baseado no problema padrão de síntese de redes proposto por Fontana (2002), propõe métodos para a redução da complexidade do problema de síntese e obtenção de redes integradas massicamente, considerando aspectos econômicos e operacionais. Inicialmente foi proposta a eliminação de variáveis inteiras do problema de otimização, transformando o problema de programação nãolinear inteira-mista (MINLP) em um problema de programação não-linear (NLP). Em seguida, foi proposta uma metodologia para a redução da complexidade do problema baseada na utilização das restrições de igualdade, reduzindo o número de variáveis de decisão. As formulações propostas apresentaram bons resultados, diminuindo consideravelmente o tempo computacional em relação ao problema MINLP original. Baseada nas metodologias desenvolvidas para redução da complexidade do problema, foi implementado ainda um gerador de estimativas iniciais viáveis utilizando números aleatórios. Também foram propostas três implementações para a síntese de redes com considerações econômicas e operacionais, resolvendo o problema de otimização em dois níveis: um externo para avaliação de critérios econômicos e um interno de onde é obtido o índice operacional. Das três formulações com considerações operacionais propostas, duas apresentaram redes com melhor desempenho operacional quando comparadas com os problemas somente com considerações econômicas. Tais resultados foram avaliados através de simulações dinâmicas com modelos linearizados, sendo observado, nestas duas implementações, aumento da robustez do sistema (redução da ação de controle sobre as variáveis manipuladas) frente a distúrbios positivos nas cargas de poluentes e mudanças nos set-points das variáveis controladas. / Water is an important raw material in the chemical, petrochemical, and food industry, being used in several stages of a process. Based on the economic importance of the water and the environmental impact through its employment in the industry, its rational consume has been receiving special attention. In the past decades, several methodologies have been proposed for the minimization of industrial water consume and wastewater emissions based on concepts of mass integration such as reuse, recycle, and regeneration of process streams. The methodologies proposed in the literature for the mass integration can be classified in two main groups: the first uses the themodynamic-heuristic-evolutive approach while the second uses mathematical programming and optimization. Both methodologies show difficulties to deal with the case of multiple pollutants: on the first one it is necessary to make some assumptions to solve this problem while the second, limitations relative to optimization methods are present. Another problem is the operational limitations due to streams recycle and reuse, that integrated processes can present. The present study, through the use of mathematical programming tools, based on the synthesis problem proposed by Fontana (2002), proposes methods to reduce the problem complexity and also for the synthesis of mass integration networks regarding economical and operational aspects. Initially it was proposed the elimination of the integer variables from the optimization problem, changing the problem from mixed-integer nonlinear programming (MINLP) to nonlinear programming (NLP). In the following, a methodology for the reduction of the problems complexity, based on the equality constraints, was applied to reduce the number of decision variables. The proposed formulations showed good results, reducing the computational time comparing to the MINLP problem. Based on the proposed methodologies for the reduction of the problem complexity described above, it was implemented a feasible initial guess generator based on random numbers. It was also proposed three formulations for the network synthesis with economic and operational considerations, solving the synthesis problem in two levels: an external level for the evaluation of economical criteria and an internal level where the operational index is obtained. Two out of the three implementations presented networks with better operational results comparing with problems only with economical aspects. These results were evaluated by dynamic simulations with linearized models and it was observed an increase in the systems robustness (reduction of the control action over the manipulated variables) when the system was subjected to positive disturbances in the pollutants loads and set-points changes.

O método do Gradiente Espectral, introduzido por Barzilai e Borwein e analisado por Raydan, para minimização irrestrita, é um método simples cujo desempenho é comparável ao de métodos tradicionais como, por exemplo, gradientes conjugados. Desde a introdução do método, assim como da sua extensão para minimização em conjuntos convexos, foram introduzidas várias combinações de passos espectrais diferentes, assim como de buscas lineares não monótonas diferentes. Dos resultados numéricos apresentados em vários trabalhos não é possível inferir se existem diferenças significativas no desempenho dos diversos métodos. Além disso, também não fica clara a relevância das buscas não monótonas como uma ferramenta em si próprias ou se, na verdade, elas são úteis apenas para permitir que o método seja o mais parecido possível com o método original de Barzilai e Borwein. O objetivo deste trabalho é comparar os diversos métodos recentemente introduzidos como combinações de diferentes buscas lineares não monótonas e diferentes passos espectrais para encontrar a melhor combinação e, a partir daí, aferir o desempenho numérico do método. / The Spectral Gradient method, introduced by Barzilai and Borwein and analized by Raydan for unconstrained minimization, is a simple method whose performance is comparable to traditional methods, such as conjugate gradients. Since the introduction of method, as well as its extension to minimization of convex sets, there were introduced various combinations of different spectral steplengths, as well as different nonmonotone line searches. By the numerical results presented in many studies it is not possible to infer whether there are siginificant differences in the performance of various methods. It also is not sure the relevance of the nonmonotone line searches as a tool in themselves or whether, in fact, they are usefull only to allow the method to be as similar as possible with the original method of Barzilai e Borwein. The objective of this study is to compare the different methods recently introduced as different combinations of nonmonotone linear searches and different spectral steplengths to find the best combination and from there, evaluating the numerical performance of the method.

No description available.

Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Technology: Department of Chemical Engineering, Durban University of Technology, 2007. / The metal finishing industry has been rated among the most polluting industries worldwide. This industry has traditionally been responsible for the release of heavy metals such as chrome, nickel, tin, copper etc into the environment. The application of cleaner production systems to a range of industries, including the metal finishing industry has provided significant financial and environmental benefits. An example of a successful application cleaner production in the metal finishing industry is the reduction in the typical water consumption from 400 1/m² to less than 10 1/m² of plated product. The successful application of cleaner production to the mental finishing industry has encountered many barriers. These barriers include the need for a highly skilled cleaner production auditor and the need for rigorous plant data to effectively quantify the cleaner production potential of the company under consideration. This study focuses on providing an alternate user-friendly audit system for the implementation of cleaner production in the mental finishing industry. The audit system proposed eliminates the need for the need for both a technical auditor and rigid plant data. The proposed system functions solely on plant operator inputs. The operator’s knowledge is harnessed and used to conduct an efficient and effective cleaner production audit. The research is based on expert knowledge, which was gained by conducting audits on some 25 companies using traditional auditing tools. This company audits were used to construct a database of data that was used in the verification of the models developed in this study. The audit is separated into different focus components. The first system developed was based on fuzzy logic multi variable decision-making. For this system the plant was categorized into different sections and appropriate fuzzy ratings were allocated based on experience. Once the allocations were completed multi variable decision analysis was used to determine the individual variable impact. The output was compared and regressed to the database equivalent. Operator inputs can then be used to determine the individual category outputs for the cleaner for the production rating for the company under consideration. The second part of this study entails the development of mathematical models for the quantification of chemical and water consumptions. This was based on the present and ideal (cleaner production) plant configuration. Cleaner production operations are compared to present operations and potential savings quantified. Mathematical models were developed based on pilot scale experiments for the acid, degreaser and zinc plating process. The pilot experiments were carried out on a PLC controlled pilot plant. These models were developed form factorial experimentation on the variables of each of the plating processes. The models developed aid in the prediction of the relevant optimum consumptions. The key challenge in traditional evaluation systems has been the quantification of the plant production. The most effective measure of production is by means of the surface area plated. In this study a novel approach using the modeled acid consumption is proposed. It was assumed that the operator inputs for the above models would not be precise. The models developed allowed for input variations. These variations were incorporated into the model using the Monte Carlo technique. The entire cleaner production evaluation system proposed is based on an operator questionnaire, which is completed in visual basic. The mathematical model was incorporated into the visual basic model. For the purpose of model verification the mathematical models were programmed and tested using the engineering mathematical software, Mat Lab. The combined fuzzy logic and mathematical models prove to be a highly effective means of completing the cleaner production evaluation in minimal time and with minimal resources. A comparative case study was conducted at a local metal finishing company. The case study compares the input requirements and outputs from the traditional systems with the system proposed in this study. The traditional model requires 245 inputs whilst the model proposed in this study is based on 56 inputs. The data requirements for the model proposed in this study is obtained from a plant operator in less than one hour whilst previous models required high level expertise over a period of up to two weeks. The quality of outputs from the model proposed is found to be very comparable to previous models. The model is actually found to be superior to previous models with regards predicting operational variations, water usages, chemical usages and bath chemical evolution. The research has highlighted the potential to apply fuzzy-mathematical hybrid systems for cleaner production evaluation. The two limitations of the research were found to be the usage of a linear experimental design for model development and the availability of Mat Lab software for future application. These issues can be addressed as future work. It is recommended that a non-linear model be developed for the individual processes so as to obtain more detailed process models. / National Research Foundation, Water Research Commission and Durban University of Technology

This dissertation aims to develop efficient algorithms with improved scalability and stability properties for large-scale optimization and optimization under uncertainty, and to bridge some of the gaps between modern optimization theories and recent applications emerging in the Big Data environment. To this end, the dissertation is dedicated to two important subjects -- i) Large-scale Convex Composite Optimization and ii) Error-in-Measurement Optimization. In spite of the different natures of these two topics, the common denominator, to be presented, lies in their accommodation for systematic use of saddle point techniques for mathematical modeling and numerical processing. The main body can be split into three parts. In the first part, we consider a broad class of variational inequalities with composite structures, allowing to cover the saddle point/variational analogies of the classical convex composite minimization (i.e. summation of a smooth convex function and a simple nonsmooth convex function). We develop novel composite versions of the state-of-the-art Mirror Descent and Mirror Prox algorithms aimed at solving such type of problems. We demonstrate that the algorithms inherit the favorable efficiency estimate of their prototypes when solving structured variational inequalities. Moreover, we develop several variants of the composite Mirror Prox algorithm along with their corresponding complexity bounds, allowing the algorithm to handle the case of imprecise prox mapping as well as the case when the operator is represented by an unbiased stochastic oracle. In the second part, we investigate four general types of large-scale convex composite optimization problems, including (a) multi-term composite minimization, (b) linearly constrained composite minimization, (c) norm-regularized nonsmooth minimization, and (d) maximum likelihood Poisson imaging. We demonstrate that the composite Mirror Prox, when integrated with saddle point techniques and other algorithmic tools, can solve all these optimization problems with the best known so far rates of convergences. Our main related contributions are as follows. Firstly, regards to problems of type (a), we develop an optimal algorithm by integrating the composite Mirror Prox with a saddle point reformulation based on exact penalty. Secondly, regards to problems of type (b), we develop a novel algorithm reducing the problem to solving a ``small series'' of saddle point subproblems and achieving an optimal, up to log factors, complexity bound. Thirdly, regards to problems of type (c), we develop a Semi-Proximal Mirror-Prox algorithm by leveraging the saddle point representation and linear minimization over problems' domain and attain optimality both in the numbers of calls to the first order oracle representing the objective and calls to the linear minimization oracle representing problem's domain. Lastly, regards to problem (d), we show that the composite Mirror Prox when applied to the saddle point reformulation circumvents the difficulty with non-Lipschitz continuity of the objective and exhibits better convergence rate than the typical rate for nonsmooth optimization. We conduct extensive numerical experiments and illustrate the practical potential of our algorithms in a wide spectrum of applications in machine learning and image processing. In the third part, we examine error-in-measurement optimization, referring to decision-making problems with data subject to measurement errors; such problems arise naturally in a number of important applications, such as privacy learning, signal processing, and portfolio selection. Due to the postulated observation scheme and specific structure of the problem, straightforward application of standard stochastic optimization techniques such as Stochastic Approximation (SA) and Sample Average Approximation (SAA) are out of question. Our goal is to develop computationally efficient and, hopefully, not too conservative data-driven techniques applicable to a broad scope of problems and allowing for theoretical performance guarantees. We present two such approaches -- one depending on a fully algorithmic calculus of saddle point representations of convex-concave functions and the other depending on a general approximation scheme of convex stochastic programming. Both approaches allow us to convert the problem of interests to a form amenable for SA or SAA. The latter developments are primarily focused on two important applications -- affine signal processing and indirect support vector machines.