【源码】用简单约束优化代价函数：有限记忆投影的拟牛顿算法

用简单约束优化代价函数：有限记忆投影的拟牛顿算法

本文描述了凸集上最小化光滑函数的优化算法。

An optimization algorithm for minimizing asmooth function over a convex set is described.

该方法的每次迭代通过使函数的对角线加低阶二次逼近在原始约束上最小化来计算下降方向。

Each iteration of the method computes adescent direction by minimizing, over the original constraints, a diagonal pluslowrank quadratic approximation to the function.

利用有限记忆准牛顿更新算法构造出二次近似。

The quadratic approximation is constructedusing a limited-memory quasi-Newton update.

该方法适用于大规模问题，其中函数的评估比投影到约束集上要复杂得多。

The method is suitable for large-scaleproblems where evaluation of the function is substantially more expensive thanprojection onto the constraint set.

对1范数正则化测试问题的数值实验表明，该方法与约束L-BFGS和正交下降等现有方法相比具有竞争力。

Numerical experiments on one-normregularized test problems indicate that the proposed method is competitive withstate-of-the-art methods such as bound constrained L-BFGS and orthant-wisedescent.

我们的进一步研究表明，该方法能够推广到一类泛化的问题，并且对于诸如学习高斯图形模型的结构和马尔可夫随机场等问题的现有方法作了实质性的改进。

We further show that the method generalizesto a wide class of problems, and substantially improves on state-of-the-artmethods for problems such as learning the structure of Gaussian graphicalmodels and Markov random fields.

一个与本文相关的英文网址供参考：

https://www.cs.ubc.ca/~schmidtm/Software/PQN.html

下载英文原文及源代码地址：

http://page2.dfpan.com/fs/blcj92213291767bd48/

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