1st Edition

Quadratic Programming with Computer Programs

By Michael J. Best Copyright 2017
    400 Pages 25 B/W Illustrations
    by CRC Press

    400 Pages 25 B/W Illustrations
    by Chapman & Hall

    400 Pages 25 B/W Illustrations
    by Chapman & Hall

    Quadratic programming is a mathematical technique that allows for the optimization of a quadratic function in several variables. QP is a subset of Operations Research and is the next higher lever of sophistication than Linear Programming. It is a key mathematical tool in Portfolio Optimization and structural plasticity. This is useful in Civil Engineering as well as Statistics.

    Geometrical Examples



    Geometry of a QP: Examples



    Geometrical Examples



    Optimality Conditions



    Geometry of Quadratic Functions



    Nonconvex QP’s



    Portfolio Opimization



    The Efficient Frontier



    The Capital Market Line



    QP Subject to Linear Equality Constraints



    QP Preliminaries



    QP Unconstrained: Theory



    QP Unconstrained: Algorithm 1



    QP with Linear Equality Constraints: Theory



    QP with Linear Equality Constraints: Alg. 2



    Quadratic Programming



    QP Optimality Conditions



    QP Duality



    Unique and Alternate Optimal Solutions



    Sensitivity Analysis



    QP Solution Algorithms



    A Basic QP Algorithm: Algorithm 3



    Determination of an Initial Feasible Point



    An Efficient QP Algorithm: Algorithm 4



    Degeneracy and Its Resolution



    A Dual QP Algorithm



    Algorithm 5



    General QP and Parametric QP Algorithms



    A General QP Algorithm: Algorithm 6



    A General Parametric QP Algorithm: Algorithm 7



    Symmetric 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



     

    Biography

    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.