[pt] Apresentamos nesta dissertação novos métodos interativos para resolver o Problema de Complementaridade Linear (PCL) e Problemas de Norma Mínima. Após uma revisão geral sobre métodos interativos para o PCL, apresentaremos no Capítulo 2, uma forma de aceleração aplicada a métodos clássicos para o PCL simétrico, através de uma decomposição (Splitting) conveniente da matriz associada ao problema. A aceleração para os novos métodos consiste em calcular uma direção de avanço usando o método básico mais uma minimização unidimensional que respeite as condições de não negatividade, provas de convergência forte são apresentadas. No Capítulo 3 comparamos algoritmos do tipo seqüencial e paralelo para solução de um Problema de Programação Linear e Problemas de Norma Mínima em l 1: para o segundo problema os métodos iterativos são aplicados no dual do problema original penalizado com um termo quadrático. Introduzimos um novo método paralelo para o Problema de Norma mínima em l 1 e provamos sua convergência. Propomos no capítulo 4, novos métodos iterativos paralelos para Problemas de Norma Mínima, convenientes para problemas de grande porte, provas de convergência são fornecidas. Finalmente, no capítulo 5 baseados sobre uma combinação da iteração de ponto proximal e métodos iterativos clássicos, propomos novos métodos iterativos para a solução de um PCL monótono não simétrico. Ilustramos todos os algoritmos apresentados, em diferentes versões, com um extensa experimentação numérica. / [en] We present in this dissertation new iterative methods for solving Linear Complementarity (LCP) and Least Norm (LNP) Problems. After a general overview on iterative methods for the LCP, in chapter 2 we present an acceleration techinique applied to classic methods for symmetric LCP generated by considering appropriate splittings of the associated matrix. The acceleration gives rise to new methods consisting of computing a search direction using the basic method plus a one dimensional minimization taking into account the nonnegative constraints. Strong convergence proofs are given. In chapter 3 we compare sequential and parallel algorithms for solving Linear Programming and least 1-Norm Problems obtained by applying iterative methods to a dual of the original problem penalized with a quadratic term. We introduce a new parallel method for the Least 1-Norm Problem, proving its convergence. In chapter 4, we present new parallel iterative methods for solving large LNP, giving convergence proofs. Finally, in chapter 5 we propose new iterative methods for solving monotone nonsymmetric LCp based on a combination of proximal point iterations and classic iterative methods. All the algorithms, in their different versions are illustrated and compared through many numerical experiments.

Current clinical practice regarding upper body prosthesis prescription and training is lacking a standarized, quantitative method to evaluate the impact of the prosthetic device. The amputee care team typically uses prior experiences to provide prescription and training customized for each individual. As a result, it is quite challenging to determine the right type and fit of a prosthesis and provide appropriate training to properly utilize it early in the process. It is also very difficult to anticipate expected and undesired compensatory motions due to reduced degrees of freedom of a prosthesis user. In an effort to address this, a tool was developed to predict and visualize the expected upper limb movements from a prescribed prosthesis and its suitability to the needs of the amputee. It is expected to help clinicians make decisions such as choosing between a body-powered or a myoelectric prosthesis, and whether to include a wrist joint. To generate the motions, a robotics-based model of the upper limbs and torso was created and a weighted least-norm (WLN) inverse kinematics algorithm was used. The WLN assigns a penalty (i.e. the weight) on each joint to create a priority between redundant joints. As a result, certain joints will contribute more to the total motion. Two main criteria were hypothesized to dictate the human motion. The first one was a joint prioritization criterion using a static weighting matrix. Since different joints can be used to move the hand in the same direction, joint priority will select between equivalent joints. The second criterion was to select a range of motion (ROM) for each joint specifically for a task. The assumption was that if the joints' ROM is limited, then all the unnatural postures that still satisfy the task will be excluded from the available solutions solutions. Three sets of static joint prioritization weights were investigated: a set of optimized weights specifically for each task, a general set of static weights optimized for all tasks, and a set of joint absolute average velocity-based weights. Additionally, task joint limits were applied both independently and in conjunction with the static weights to assess the simulated motions they can produce. Using a generalized weighted inverse control scheme to resolve for redundancy, a human-like posture for each specific individual was created. Motion capture (MoCap) data were utilized to generate the weighting matrices required to resolve the kinematic redundancy of the upper limbs. Fourteen able-bodied individuals and eight prosthesis users with a transradial amputation on the left side participated in MoCap sessions. They performed ROM and activities of daily living (ADL) tasks. The methods proposed here incorporate patient's anthropometrics, such as height, limb lengths, and degree of amputation, to create an upper body kinematic model. The model has 23 degrees-of-freedom (DoFs) to reflect a human upper body and it can be adjusted to reflect levels of amputation. The weighting factors resulted from this process showed how joints are prioritized during each task. The physical meaning of the weighting factors is to demonstrate which joints contribute more to the task. Since the motion is distributed differently between able-bodied individuals and prosthesis users, the weighting factors will shift accordingly. This shift highlights the compensatory motion that exist on prosthesis users. The results show that using a set of optimized joint prioritization weights for each specific task gave the least RMS error compared to common optimized weights. The velocity-based weights had a slightly higher RMS error than the task optimized weights but it was not statistically significant. The biggest benefit of that weight set is their simplicity to implement compared to the optimized weights. Another benefit of the velocity based weights is that they can explicitly show how mobile each joint is during a task and they can be used alongside the ROM to identify compensatory motion. The inclusion of task joint limits gave lower RMS error when the joint movements were similar across subjects and therefore the ROM of each joint for the task could be established more accurately. When the joint movements were too different among participants, the inclusion of task limits was detrimental to the simulation. Therefore, the static set of task specific optimized weights was found to be the most accurate and robust method. However, the velocity-based weights method was simpler with similar accuracy. The methods presented here were integrated in a previously developed graphical user interface (GUI) to allow the clinician to input the data of the prospective prosthesis users. The simulated motions can be presented as an animation that performs the requested task. Ultimately, the final animation can be used as a proposed kinematic strategy that a prosthesis user and a clinician can refer to, during the rehabilitation process as a guideline. This work has the potential to impact current prosthesis prescription and training by providing personalized proposed motions for a task.