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We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. Our framework is very flexible and includes both fully parallel Jacobi schemes and Gauss–Seidel (i.e., sequential) ones, as well as virtually all possibilities “in between” with only a subset of variables updated at each iteration. Our theoretical convergence results improve on existing ones, and numerical results on LASSO, logistic regression, and some nonconvex quadratic problems show that the new method consistently outperforms existing algorithms.

In this paper we present an integrated approach to COSMO-SkyMed image analysis and classification exploiting integration of different data of the regions of interest, namely urban forestry areas, wide urban parks. The aim is to provide a methodology for exploiting complex data structures built upon multi resolution grids gathering together with optical and X-SAR images, also historical land exploitation and meteorological data, records of human habits, and several other information sources. Although these data are specifically gathered to built a fire susceptibility map, the method is quite general. Indeed, the contribution of the model and its novelty relies manly on the definition of a learning schema lifting different factors and aspects of the event to be identified (here fire causes), including physical, social and behavioral ones, to the design of a fire susceptibility map, of a specific urban forestry. The outcome is an integrated geospatial database providing an infrastructure that merges cartography, heterogeneous data and complex analysis, in so establishing a digital environment where users and tools are interactively connected in an efficient and flexible way.