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, especially 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 unconstrained and constrained optimization problems. Natural algorithms are then developed from these optimality conditions, and their most important convergence charact-eristics are analyzed. The book answers many more questions of the form “Why/why not?” than “How?”. This choice of focus is in contrast to books main-ly providing numerical guidelines as to how optimization problems should be solved. 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 under graduate students, and has already been used as such, in the form of lecture notes, for nearly ten years.
The book can be used in optimization courses at any engineering department as well as in mathematics, 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.
NICLAS ANDREASSON is a licentiate of technology in applied mathematics at Chalmers University of Technology, Gothenburg.
ANTON EVGRAFOV is a doctor of philosophy in applied mathematics from Chalmers University of Technology, and is presently at Center for Aerospace Structures at University of Colorado at Boulder.
MICHAEL PATRIKSSON is a professor in applied mathematics at Chalmers University of Technology, Gothenburg.
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