Quadratic Programming with Computer Programs

Michael J. Best (Autor)

Buch | Hardcover

386 Seiten

2017
Chapman & Hall/CRC (Verlag)
978-1-4987-3575-9 (ISBN)

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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.

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.

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

Erscheinungsdatum	15.03.2017
Reihe/Serie	Advances in Applied Mathematics
Zusatzinfo	25 Illustrations, black and white
Sprache	englisch
Maße	178 x 254 mm
Gewicht	882 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	1-4987-3575-4 / 1498735754
ISBN-13	978-1-4987-3575-9 / 9781498735759
Zustand	Neuware