A Semi-smooth, Self-shifting, and Singular Newton Method for Sparse Optimal Transport
Primary Area: optimization
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Keywords: Newton's method, semi-smooth function, non-isolated solution, global convergence, quadratic convergence, optimal transport
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TL;DR: A novel Newton-type optimization method for non-smooth and singular problems, useful in solving sparse optimal transport problems.
Abstract: Newton's method is an important second-order optimization algorithm that has been extensively studied. However, many challenging optimization problems break the classical assumptions of Newton's method. For example, the objective function may not be twice differentiable, and the optimal solution may be non-unique. In this article, we propose a general Newton-type algorithm named S5N, to solve problems that have possibly non-differentiable gradients and non-isolated solutions, a setting highly motivated by the sparse optimal transport problem. Compared with existing Newton-type approaches, the proposed S5N algorithm has broad applicability, does not require hyperparameter tuning, and possesses rigorous global and local convergence guarantees. Extensive numerical experiments show that on sparse optimal transport problems, S5N gains superior performance on convergence speed and computational efficiency.
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Submission Number: 5242
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