Linear and Nonlinear Programming

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This new edition emphasizes state-of-the-art practical optimization techniques, highlighting the connection between the analytical nature of optimization problems and the algorithms used to solve them. The material is organized into three parts. Part I serves as a self-contained introduction to linear programming, covering key theoretical elements, effective numerical algorithms, and significant applications. Part II, independent of Part I, delves into unconstrained optimization theory, presenting optimality conditions and basic algorithms while exploring algorithm properties and convergence notions. Part III extends these concepts to constrained optimization problems and can be approached without prior knowledge from Part I, as used in various universities. A notable addition is a chapter on Conic Linear Programming, an advanced topic with diverse applications. The edition also introduces an accelerated steepest descent method with superior convergence properties, along with proofs for both standard and accelerated methods. End-of-chapter exercises are included for all chapters. Reviews of the previous edition praise it as a classic textbook in optimization, essential for students, researchers, and specialists across various disciplines.