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