Quadratic Programming with Computer Programs

1. Auflage 2017
ISBN: 978-1-4987-3575-9
Verlag: Taylor & Francis Inc

Buch, Englisch, 400 Seiten, Format (B × H): 263 mm x 190 mm, Gewicht: 868 g

Reihe: Advances in Applied Mathematics

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.

Autoren/Hrsg.

Best, Michael J.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Technische Wissenschaften Bauingenieurwesen Bauingenieurwesen

Inhaltsverzeichnis

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

Über Autor(innen)

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.