Many important machine learning, computer vision and image processing problems can be cast as convex energy minimization problems, e.g. training of SVMs, logistic regression, low-rank and sparse matrix decomposition, denoising, segmentation, or multiframe blind deconvolution. In this lecture we will discuss first order convex optimization methods to implement and solve the aforementioned problems efficiently. Particular attention will be paid to problems including constraints and non-differentiable terms, giving rise to methods that exploit the concept of duality such as the primal-dual hybrid gradient method or the alternating directions methods of multipliers. This lecture will cover the mathematical background needed to understand why the investigated methods converge as well as the efficient practical implementation. | Many important machine learning, computer vision and image processing problems can be cast as convex energy minimization problems, e.g. training of SVMs, logistic regression, low-rank and sparse matrix decomposition, denoising, segmentation, or multiframe blind deconvolution. In this lecture we will discuss first order convex optimization methods to implement and solve the aforementioned problems efficiently. Particular attention will be paid to problems including constraints and non-differentiable terms, giving rise to methods that exploit the concept of duality such as the primal-dual hybrid gradient method or the alternating directions methods of multipliers. This lecture will cover the mathematical background needed to understand why the investigated methods converge as well as the efficient practical implementation. |