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.

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