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We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which isa provably convergent, second order incremental algorithm for solvinglarge-scale partially separable optimization problems. The algorithm is basedon a local quadratic approximation, and hence, allows incorporating curvatureinformation to speed-up the convergence. HAMSI is inherently parallel and itscales nicely with the number of processors. Combined with techniques foreffectively utilizing modern parallel computer architectures, we illustratethat the proposed method converges more rapidly than a parallel stochasticgradient descent when both methods are used to solve large-scale matrixfactorization problems. This performance gain comes only at the expense ofusing memory that scales linearly with the total size of the optimizationvariables. We conclude that HAMSI may be considered as a viable alternative inmany large scale problems, where first order methods based on variants ofstochastic gradient descent are applicable.

HAMSI: A Parallel Incremental Optimization Algorithm Using Quadratic Approximations for Solving Partially Separable Problems