This is a book for people interested in solving optimization problems. Because of the wide (and growing) use of optimization in science, engineering, economics, and industry, it is essential for students and practitioners alike to develop an understanding of optimization algorithms. Knowledge of the capabilities and limitations of these algorithms leads to a better understanding of their impact on various applications, and points the way to future research on improving and extending optimization algorithms and software. Our goal in this book is to give a comprehensive description of the most powerful, state-of-the-art, techniques for solving continuous optimization problems. By presenting the motivating ideas for each algorithm, we try to stimulate the reader's intuition and make the technical details easier to follow. Formal mathematical requirements are kept to a minimum. Because of our focus on continuous problems, we have omitted discussion of important optimization topics such as discrete and stochastic optimization
CONTENT
Fundamentals of Unconstrained Optimization -- Line Search Methods -- Trust-Region Methods -- Conjugate Gradient Methods -- Practical Newton Methods -- Calculating Derivatives -- Quasi-Newton Methods -- Large-Scale Quasi-Newton and Partially Separable Optimization -- Nonlinear Least-Squares Problems -- Nonlinear Equations -- Theory of Constrained Optimization -- Linear Programming: The Simplex Method -- Linear Programming: Interior-Point Methods -- Fundamentals of Algorithms for Nonlinear Constrained Optimization -- Quadratic Programming -- Penalty, Barrier, and Augmented Lagrangian Methods -- Sequential Quadratic Programming
Mathematics
Operations research
Decision making
System theory
Calculus of variations
Mathematics
Calculus of Variations and Optimal Control; Optimization
