Introductory Lectures on Convex Optimization - A Basic Course
Introductory Lectures on Convex Optimization - A Basic Course
复制标题
DOI：
10.1007/978-1-4419-8853-9
复制
发表时间：
2014-04
期刊：
影响因子：
--
通讯作者：
Y. Nesterov
中科院分区：
文献类型：
--
作者：
Y. Nesterov
这是在20世纪80年代中期，当开创性的论文卡尔markar开辟了一个新的时代，在非线性优化。本文的重要性不仅在于它的复杂性上，而且还在于它的一个新的多项式时间算法。当时，该算法最令人惊讶的特点是其高效率的理论预测得到了良好的计算结果的支持。这一不寻常的事实极大地改变了非线性优化研究的风格和方向。此后，它变得越来越普遍，新的方法提供了一个复杂性分析，这被认为是一个更好的理由，他们的效率比计算实验。在一个新的迅速发展的领域，这得到了名称“多项式时间的邻域点方法”，这样的理由是强制性的。经过近十五年的深入研究，这一发展的主要成果开始出现在专著中[12，14，16，17，18，19]。大约在那个时候，作者被要求准备一个新的课程非线性优化的研究生。其想法是开设一门反映该领域新发展的课程。其实，这是一个很大的挑战。当时，只有线性最优化的边界点法的理论才足够完善，可以向学生解释。自谐函数的一般理论只以研究专著的形式出现过一次[12]。
It was in the middle of the 1980s, when the seminal paper by Kar markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly develop ing field, which got the name" polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].