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This is an overview paper written in style of research proposal. In recent years we introduced a general framework for large-scale unconstrained optimization -- Sequential Subspace Optimization (SESOP) and demonstrated its usefulness for sparsity-based signal/image denoising, deconvolution, compressive sensing, computed tomography, diffraction imaging, support vector machines. We explored its combination with Parallel Coordinate Descent and Separable Surrogate Function methods, obtaining statearXiv:1401.0159v1 fatcat:j4pysvjrqjfz7ozapzxpn7tj4a