An introduction to continuous optimization : foundations and fundamental algorithms

Optimization, or mathematical programming, is a fundamental subject within decision science and operations research, in which mathematical decision models are constructed, analyzed, and solved.The book”s focus lies on providing a basis for the analysis of optimization models and of candidate optimal solutions for continuous optimization models. The main part of the mathematical material therefore concerns the analysis and linear algebra that underlie the workings of convexity and duality, and necessary/sufficient local/global optimality conditions for continuous optimization problems. Natural algorithms are then developed from these optimality conditions, and their most important convergence characteristics are analyzed. The book answers many more questions of the form ”Why?” and ”Why not?” than ”How?”. We use only elementary mathematics in the development of the book, yet are rigorous throughout.The book provides lecture, exercise and reading material for a first course on continuous optimization and mathematical programming, geared towards third-year students, and has already been used as such for nearly ten years. The preface to the second edition describes the main changes made since the first, 2005, edition.The book can be used in mathematical optimization courses at any mathematics, engineering, economics, and business schools. It is a perfect starting book for anyone who wishes to develop his/her understanding of the subject of optimization, before actually applying it.Second edition