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

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