这本书详细而严格地论述了有限维空间中的优化理论（无约束优化、非线性规划、半无限规划等）。本文详细介绍了非线性规划中的凸性理论、对偶理论、线性不等式、凸多面体和线性规划的基本结果。
200多个精心挑选的练习应该有助于学生掌握本书的内容，并提供进一步的见解。为了给讲师提供灵活性，一些最基本的结果以几种独立的方式得到了证明。另一章详细介绍了三种最基本的优化算法（最速下降法、牛顿法、共轭梯度法）。书的第一章介绍了书中使用的必要的微分学工具。有几章包含优化方面更高级的主题，如Ekeland的epsilon变分原理、对一般向量空间中两个或多个凸集的分离性质的深入而详细的研究、Helly定理及其在优化中的应用等。这本书适合作为研究生一级或二级优化课程的教科书。它也适合自学或作为高级读者的参考书。这本书源于作者自1993年以来十几次教授研究生一学期课程的经验。奥斯曼·古勒是巴尔的摩县马里兰大学数学与统计系教授。他的研究兴趣包括数学规划、凸分析、优化问题的复杂性和运筹学。
Foundations of Optimization
The book gives a detailed and rigorous treatment of the theory of optimization (unconstrained optimization, nonlinear programming, semi-infinite programming, etc.) in finite-dimensional spaces. The fundamental results of convexity theory and the theory of duality in nonlinear programming and the theories of linear inequalities, convex polyhedra, and linear programming are covered in detail.
Over two hundred, carefully selected exercises should help the students master the material of the book and give further insight. Some of the most basic results are proved in several independent ways in order to give flexibility to the instructor. A separate chapter gives extensive treatments of three of the most basic optimization algorithms (the steepest-descent method, Newton’s method, the conjugate-gradient method). The first chapter of the book introduces the necessary differential calculus tools used in the book. Several chapters contain more advanced topics in optimization such as Ekeland’s epsilon-variational principle, a deep and detailed study of separation properties of two or more convex sets in general vector spaces, Helly’s theorem and its applications to optimization, etc. The book is suitable as a textbook for a first or second course in optimization at the graduate level. It is also suitable for self-study or as a reference book for advanced readers. The book grew out of author’s experience in teaching a graduate level one-semester course a dozen times since 1993. Osman Guler is a Professor in the Department of Mathematics and Statistics at University of Maryland, Baltimore County. His research interests include mathematical programming, convex analysis, complexity of optimization problems, and operations research.
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