Nonlinear Convex Optimization with Applications in Imaging and Vision
Undergraduate and Graduate course, University of Siegen, 2025
Summer term 2025 (~ 4 students per semester).
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Convex sets and functions
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Gradient descent and its convergence
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Variants: projected, proximal, and forward-backward splitting
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Newton and quasi-Newton methods
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Subdifferentials and KKT conditions
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Quadratic programming and interior point methods
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Duality and sequential quadratic programming
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Nonsmooth Newton methods: NCP, patchwise, semismooth
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Primal-dual hybrid gradient methods
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Proximal Newton methods for unconstrained problems