Quadratic Programming with Computer Programs

Michael J. Best is Professor Emeritus in the Department of Combinatorics and Optimization at the University of Waterloo. He is only the second person to receive a B.Math degree from the University of Waterloo and holds a PhD from UC-Berkeley. Michael is also the author of Portfolio Optimzation, published by CRC Press.

This book is devoted to quadratic programming (QP) and parametric quadratic programming (PQP). It is a textbook which may be useful for students and many scientific researchers as well. It is richly illustrated with many examples and gures.The book starts with the presentation of some geometric facts on unconstrained QP problems, followed by the introduction of some QP models arising in portfolio optimization. The latter reflects the author's experience with such types of applications.The rest of the book is organized logically as is usually done in QP: unconstrained convex QP problems, QP with linear equality constraints, QP with linear inequality constraints, duality in quadratic programming, dual QP algorithms, general QP and PQP algorithms, the simplex method for QP and PQP and nonconvex QP.Andrzej Stachurski~Mathematical Reviews, 2017

• Geometrical ExamplesGeometry of a QP: ExamplesGeometrical ExamplesOptimality ConditionsGeometry of Quadratic FunctionsNonconvex QP’sPortfolio Opimization The Efficient FrontierThe Capital Market Line QP Subject to Linear Equality ConstraintsQP PreliminariesQP Unconstrained: TheoryQP Unconstrained: Algorithm 1QP with Linear Equality Constraints: TheoryQP with Linear Equality Constraints: Alg. 2 Quadratic ProgrammingQP Optimality ConditionsQP DualityUnique and Alternate Optimal SolutionsSensitivity AnalysisQP Solution AlgorithmsA Basic QP Algorithm: Algorithm 3 Determination of an Initial Feasible PointAn Efficient QP Algorithm: Algorithm 4Degeneracy and Its ResolutionA Dual QP Algorithm Algorithm 5 General QP and Parametric QP Algorithms A General QP Algorithm: Algorithm 6 A General Parametric QP Algorithm: Algorithm 7Symmetric Matrix Updates Simplex Method for QP and PQP Simplex Method for QP: Algorithm 8 Simplex Method for Parametric QP: Algorithm 9 Nonconvex Quadratic Programming Optimality Conditions Finding a Strong Local Minimum: Algorithm 10