Optimization—Theory and Practice

Dr. Wilhelm Forst is a professor in the Department of Numerical Analysis at the University of Ulm, Germany. Dr. Dieter Hoffmann is a professor at the University of Konstanz, Germany. Drs. Forst and Hoffman previously co-authored two German language books for Springer-Verlag: Funktionentheorie explore with Maple (2002) and Ordinary Differential Equations (2005).

1. Introduction: Examples of Optimization Problems, Historical
Overview.- 2. Optimality Conditions: Convex Sets, Inequalities, Local
First- and Second-Order Optimality Conditions, Duality.- 3. Unconstrained Optimization Problems: Elementary Search and Localization Methods, Descent Methods with Line Search, Trust Region Methods, Conjugate Gradient Methods, Quasi-Newton Methods.- 4. Linearly Constrained Optimization Problems: Linear and Quadratic Optimization, Projection Methods.- 5. Nonlinearly Constrained Optimization Methods: Penalty Methods, SQP Methods.- 6. Interior-Point Methods for Linear Optimization: The Central Path, Newton's Method for the Primal-Dual System, Path-Following Algorithms, Predictor-Corrector Methods.- 7. Semidefinite Optimization:
Selected Special Cases, The S-Procedure, The Function log°det, Path-Following Methods, How to Solve SDO Problems?, Icing on the
Cake: Pattern Separation via Ellipsoids.- 8. Global Optimization:
Branch and Bound Methods, Cutting Plane Methods.- Appendices:
A Second Look at the Constraint Qualifications, The Fritz John Condition, Optimization Software Tools for Teaching and Learning.-
Bibliography.- Index of Symbols.- Subject Index.