Zero-norm optimization: Models and applications



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A zero-norm optimization model is a mathematical program in which one either minimizes or restricts the number of certain sets of variables to being non-zero. Zero-norm optimization arises in various applications, such as compressive sensing, metabolic engineering, portfolio optimization and data mining. In these examples we find the most common form of zero-norm optimization: we minimize or restrict the number of allowed activities by minimizing or restricting the number of the respective {\em activity variables} that are allowed to being non-zero. In this thesis we study recent applications of zero-norm and models related to these optimization problems. We first discuss the applications and thereafter study the problem statement of the applications. Once the problem statement is understood we then see how the zero-norm model can be tackled to solve the problem.



Zero-norm, NP-hard constraints