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arXiv · 1904.03563

A Log-Barrier Newton-CG Method for Bound Constrained Optimization with Complexity Guarantees

Michael O'Neill·Stephen J. Wright
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Abstract

We describe an algorithm based on a logarithmic barrier function, Newton's method, and linear conjugate gradients that obtains an approximate minimizer of a smooth function over the nonnegative orthant. We develop a bound on the complexity of the approach, stated in terms of the required accuracy and the cost of a single gradient evaluation of the objective function and/or a matrix-vector multiplication involving the Hessian of the objective. The approach can be implemented without explicit calculation or storage of the Hessian.

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Michael O'Neill, Stephen J. Wright. 2019-12-03. A Log-Barrier Newton-CG Method for Bound Constrained Optimization with Complexity Guarantees. https://arxiv.org/abs/1904.03563

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