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.
