非线性规划(第3版清华版双语教学用书)(英文版)

伯特瑟卡斯著的《非线性规划(第3版清华版双语 教学用书)(英文版)》涵盖非线性规划的主要内容， 包括无约束优化、凸优化、拉格朗日乘子理论和算法 、对偶理论及方法等，包含了大量的实际应用案例。 本书从无约束优化问题入手，通过直观分析和严格证 明给出了无约束优化问题的最优性条件，并讨论了梯 度法、牛顿法、共轭方向法等基本实用算法。进而本 书将无约束优化问题的最优性条件和算法推广到具有 凸集约束的优化问题中，进一步讨论了处理约束问题 的可行方向法、条件梯度法、梯度投影法、双度量投 影法、近似算法、流形次优化方法、坐标块下降法等 。拉格朗日乘子理论和算法是非线性规划的核心内容 之一，也是本书的重点。

Dimitri P.Bertsekas ，美国工程院院士，IEEE会士。1971年获MIT电子工程博士学位。长期在MIT执教，曾获得2001年度美国控制协会J.Ragazzini教育奖。其研究领域涉及优化、控制、大规模计算、数据通信网络等，许多研究具有开创性贡献。著有Nonlinear Programming等十余部教材和专著，其中许多被MIT等名校用作研究生或本科生教材。

1. Unconstrained Optimization: Basic Methods 1.1. Optimality Conditions 1.1.1. Variational Ideas 1.1.2. Main Optimality Conditions 1.2. Gradient Methods – Convergence 1.2.1. Descent Directions and Stepsize Rules 1.2.2. Convergence Results 1.3. Gradient Methods –Rate of Convergence 1.3.1. The Local Analysis Approach 1.3.2. The Role of the Condition Number 1.3.3. Convergence Rate Results 1.4. Newton's Method and Variations 1.4.1. Modified Cholesky Factorization 1.4.2. Trust Region Methods 1.4.3. Variants of Newton's Method 1.4.4. Least Squares and the Gauss-Newton Method 1.5. Notes and Sources 2. Unconstrained Optimization: Additional Methods 2.1. Conjugate Direction Methods 2.1.1. The Conjugate Gradient Method 2.1.2. Convergence Rate of Conjugate Gradient Method 2.2. Quasi-Newton Methods 2.3. Nonderivative Methods 2.3.1. Coordinate Descent 2.3.2. Direct Search Methods 2.4. Incremental Methods 2.4.1. Incremental Gradient Methods 2.4.2. Incremental Aggregated Gradient Methods 2.4.3. Incremental Gauss-Newton Methods 2.4.3. Incremental Newton Methods 2.5. Distributed Asynchronous Algorithms 2.5.1. Totally andPartiallyAsynchronousAlgorithms 2.5.2. TotallyAsynchronousConvergence 2.5.3. PartiallyAsynchronousGradient-LikeAlgorithms 2.5.4. ConvergenceRate ofAsynchronousAlgorithms 2.6. Discrete-TimeOptimalControlProblems 2.6.1. Gradient andConjugateGradientMethods for OptimalControl 2.6.2. Newton's Method for Optimal Control 2.7. SolvingNonlinearProgrammingProblems - Some PracticalGuidelines 2.8. Notes and Sources 3. Optimization Over a Convex Set 3.1. ConstrainedOptimizationProblems 3.1.1. Necessary and Sufficient Conditions for Optimality 3.1.2. Existence of Optimal Solutions 3.2. Feasible Directions -Conditional Gradient Method 3.2.1. Descent Directions and StepsizeRules 3.2.2. The Conditional Gradient Method 3.3. Gradient Projection Methods 3.3.1. Feasible Directions and Stepsize Rules Basedon Projection 3.3.2. Convergence Analysis