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        Methods for eigenvalue optimization with application to semidefinite optimization

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        Publication date
        2015
        Author
        Broeders, E.J.
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        Summary
        This thesis deals with eigenvalue optimization problems and some methods which are applicable in solving those kind of problems. The goal is to develop a novel algorithm which can solve large instances of eigenvalue optimization problems. In the second chapter is shown how semidefinite optimization problems can be turned into eigenvalue optimization problems through a rotation of basis. Although the relation between semidefinite optimization and eigenvalue opti- mization is not new, this approach where a semidefinite optimization problem is turned into a full eigenvalue optimization problem is. In the third chapter SASPA (Subspace Accelerated Sensitive Pole Algorithm) is used to compute the intersection points of eigencurves. This is a novel appli- cation which allows to compute such intersection points with less computation time than through bisection methods. Moreover, SASPA also works for non- simple eigenvalues. The fourth chapter deals with developing a novel algorithm to solve eigen- value optimization problems based on gradients. This algorithm is able to handle large sparse problems within reasonable computation time.
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        https://studenttheses.uu.nl/handle/20.500.12932/28733
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