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During recent years there has been an increased interest in stochasticadaptations of limited memory quasi-Newton methods, which compared to puregradient-based routines can improve the convergence by incorporating secondorder information. In this work we propose a direct least-squares approachconceptually similar to the limited memory quasi-Newton methods, but thatcomputes the search direction in a slightly different way. This is achieved ina fast and numerically robust manner by maintaining a Cholesky factor of lowdimension. This is combined with a stochastic line search relying uponfulfilment of the Wolfe condition in a backtracking manner, where the steplength is adaptively modified with respect to the optimisation progress. Wesupport our new algorithm by providing several theoretical results guaranteeingits performance. The performance is demonstrated on real-world benchmarkproblems which shows improved results in comparison with already establishedmethods.

A fast quasi-Newton-type method for large-scale stochastic optimisation