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The complexity of automated systems has grown considerably during the past decades. This convolutes the observation of possible faults in these systems. If not being revealed timely, such faults can lead to catastrophic failures. As a result, there is a continuous interest in sophisticated fault diagnosis techniques. Since it is generally desired to diagnose faults in the earliest possible stages, computational challenges are imposed on the algorithms. Whereas the field of fault diagnosis comprises of a large variety of techniques in various categories, these computational challenges appear to emerge wide-ranging.

At the same time, convex optimization has developed as a valuable tool to solve a large variety of mathematical problems with computational efficiency. This computational efficiency is achieved by exploiting favorable structures of the problem. Depending on the specific problem, these structures vary in difficulty to be recognized or arranged. Moreover, some problems lead to a convex optimization problem naturally, while other problems first need some kind of relaxation or sequential process in order to employ convex optimization. This thesis explores how convex optimization can be utilized in order to solve fault diagnosis problems with computational efficiency.

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