During the six years since the first edition of this book appeared, the field of continuous optimization has continued to grow and evolve. This new edition reflects a better understanding of constrained optimization at both the algorithmic and theoretical levels, and of the demands imposed by practical applications. Perhaps most notably, new chapters have been added on two important topics: derivative-free optimization (Chapter 9) and interior-point methods for nonlinear programming (Chapter 19). The former topic has proved to be of great interest in applications, while the latter topic has come into its own in recent years and now forms the basis of successful codes for nonlinear programming.
Apart from the new chapters, we have revised and updated throughout the book, de-emphasizing or omitting less important topics, enhancing the treatment of subjects of evident interest, and adding new material in many places. The first part (unconstrained optimization) has been comprehensively reorganized to improve clarity. Discussion of Newton’s method—the touchstone method for unconstrained problems—is distributed more naturally throughout this part rather than being isolated in a single chapter. An expanded discussion of large-scale problems appears in Chapter 7.
Some reorganization has taken place also in the second part (constrained optimization), with material common to sequential quadratic programming and interior-point methods now appearing in the chapter on fundamentals of nonlinear programming algorithms (Chapter 15) and the discussion of primal barrier methods moved to the new interior-point chapter. There is much new material in this part, including a treatment of nonlinear programming duality, an expanded discussion of algorithms for inequality constrained quadratic programming, a discussion of dual simplex and presolving in linear programming, a summary of practical issues in the implementation of interior-point linear programming algorithms, a description of conjugate-gradient methods for quadratic programming, and a discussion of filter methods and nonsmooth penalty methods in nonlinear programming algorithms.
In many chapters we have added a Perspectives and Software section near the end, to place the preceding discussion in context and discuss the state of the art in software. The appendix has been rearranged with some additional topics added, so that it can be used in a more stand-alone fashion to cover some of the mathematical background required for the rest of the book. The exercises have been revised in most chapters. After these many additions, deletions, and changes, the second edition is only slightly longer than the first, reflecting our belief that careful selection of the material to include and exclude is an important responsibility for authors of books of this type.
A manual containing solutions for selected problems will be available to bona fide instructors through the publisher. A list of typos will be maintained on the book’s web site, which is accessible from the web pages of both authors.
We acknowledge with gratitude the comments and suggestions of many readers of the first edition, who sent corrections to many errors and provided valuable perspectives on the material, which led often to substantial changes. We mention in particular Frank Curtis, Michael Ferris, Andreas Griewank, Jacek Gondzio, Sven Leyffer, Philip Loewen, Rembert Reemtsen, and David Stewart.
Our special thanks goes to Michael Overton, who taught from a draft of the second edition and sent many detailed and excellent suggestions. We also thank colleagues who read various chapters of the new edition carefully during development, including Richard Byrd, Nick Gould, Paul Hovland, Gabo Lope ́z-Calva, Long Hei, Katya Scheinberg, Andreas Wa ̈chter, and Richard Waltz. We thank Jill Wright for improving some of the figures and for the new cover graphic.
We mentioned in the original preface several areas of optimization that are not covered in this book. During the past six years, this list has only grown longer, as the field has continued to expand in new directions. In this regard, the following areas are particularly noteworthy: optimization problems with complementarity constraints, second-order cone and semidefinite programming, simulation-based optimization, robust optimization, and mixed-integer nonlinear programming. All these areas have seen theoretical and algorithmic advances in recent years, and in many cases developments are being driven by new classes of applications. Although this book does not cover any of these areas directly, it provides a foundation from which they can be studied.
自本书第一版问世以来的六年中，持续优化领域一直在不断发展和演变。这个新版本反映了在算法和理论层面上更好地理解约束优化，以及实际应用所带来的要求。也许最值得注意的是，在两个重要的主题上增加了新的章节：无导数优化（第9章）和非线性规划的内点方法（第19章）。前一个主题已经被证明是非常有趣的应用，而后一个主题在最近几年已经形成了自己的主题，现在已经形成了成功的非线性规划代码的基础。
除了新的章节，我们在整本书中进行了修订和更新，淡化或省略了不太重要的主题，加强了对明显感兴趣的主题的处理，并在许多地方增加了新的材料。第一部分（无约束优化）已全面重组，以提高清晰度。牛顿法的讨论无约束问题的试金石方法在这一部分更自然地分布，而不是孤立在一章中。关于大规模问题的扩展讨论出现在第7章。
在第二部分（约束优化）中也进行了一些重组，随着序列二次规划和内点方法的共同材料现在出现在非线性规划算法的基础章节（第15章）和原始障碍法的讨论转移到新的内点章节。在对偶规划的一个新的讨论中，包含了一个新的非线性二次规划算法的讨论，概述了内点线性规划算法实现中的实际问题，描述了二次规划的共轭梯度法，讨论了非线性规划算法中的滤波方法和非光滑惩罚方法。
在许多章节中，我们在结尾处增加了一个透视图和软件部分，将前面的讨论放在上下文中并讨论软件的最新技术。附录已经重新安排，增加了一些附加的主题，这样它就可以以一种更独立的方式来涵盖本书其余部分所需的一些数学背景知识。练习题在大多数章节都作了修改。经过这么多的增删和修改，第二版只比第一版稍长，这反映了我们的信念，即仔细选择要包括和排除的材料是这类书籍作者的重要责任。
一本包含所选问题解决方案的手册将通过出版商提供给真正的教师。这本书的网站上会有一份打字错误的清单，可以从两位作者的网页上找到。
我们感谢第一版的许多读者的评论和建议，他们对许多错误进行了更正，并对材料提供了宝贵的观点，这常常导致实质性的变化。我们特别提到弗兰克·柯蒂斯、迈克尔·费里斯、安德烈亚斯·格里旺克、杰克冈齐奥、斯文·莱弗、菲利普·洛文、伦伯特·里姆森和大卫·斯图尔特。
我们要特别感谢迈克尔·奥弗顿，他从第二版的草稿中教书，并提出了许多详细而优秀的建议。我们也要感谢在开发过程中仔细阅读新版各章的同事，包括理查德·伯德、尼克·古尔德、保罗·霍夫兰、加博·洛普́z-Calva、Long Hei、Katya Scheinberg、Andreas Wáchter和Richard Waltz。我们感谢吉尔莱特改进了一些数字和新的封面图片。
我们在最初的序言中提到了本书中未涉及的几个优化领域。在过去的六年里，随着该领域不断向新的方向扩展，这份名单只增长了一些。在这方面，特别值得注意的领域有：互补约束优化问题、二阶锥半定规划、基于仿真的优化、鲁棒优化和混合整数非线性规划。近年来，所有这些领域在理论和算法上都取得了进展，在许多情况下，新的应用类别正在推动发展。虽然这本书并没有直接覆盖这些领域，但它提供了一个可以研究的基础。
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