A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems
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2007-01-01
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Proceedings of the ... American Control Conference. American Control Conference
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IEEE
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Electrical and Electronic Engineering
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Conference Paper
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Ji, H., Huang, M., Moore, J. B. & Manton, J. H. (2007). A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems. Proceedings of the American Control Conference, pp.540-545. IEEE. https://doi.org/10.1109/ACC.2007.4282797.
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American Control Conference
Abstract
Self-concordant functions are a special class of convex functions introduced by Nesterov and Nemirovskii and used in interior point methods. This paper proposes a damped conjugate gradient method for optimization of self-concordant functions. This method is an ordinary conjugate gradient method but with a novel step-size selection rule which is proved to ensure the algorithm converges to the global minimum. As an example, the algorithm is applied to a quadratically constrained quadratic optimization problem.
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Artificial Intelligence and Image Processing