We describe an algorithm based on a logarithmic barrier function, Newton’s method and linear conjugate gradients that seeks an approximate minimizer of a smooth function over the non-negative 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.

中文翻译：

---

对数约束牛顿-CG方法，用于具有复杂性保证的约束约束优化

我们描述了一种基于对数势垒函数，牛顿法和线性共轭梯度的算法，该算法在非负正整数上寻求平滑函数的近似最小化器。我们根据所需精度和目标函数的单个梯度评估和/或涉及目标Hessian的矩阵向量乘法的成本，确定了方法的复杂性。无需显式计算或存储Hessian即可实施该方法。