Quadratic Programming With Computer Programs (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. Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Using the Matlab Programs -- 1 Geometrical Examples -- 1.1 Geometry of a QP: Examples -- 1.2 Optimality Conditions -- 1.3 Geometry of Quadratic Functions -- 1.4 Nonconvex QP's -- 1.5 Exercises -- 2 Portfolio Optimization -- 2.1 The Efficient Frontier -- 2.2 The Capital Market Line -- 2.3 Computer Programs -- 2.4 Exercises -- 3 QP Subject to Linear Equality Constraints -- 3.1 QP Preliminaries -- 3.2 QP Unconstrained: Theory -- 3.3 QP Unconstrained: Algorithm 1 -- 3.4 QP With Linear Equality Constraints: Theory -- 3.5 QP With Linear Equality Constraints: Algorithm 2 -- 3.6 Computer Programs -- 3.7 Exercises -- 4 Quadratic Programming Theory -- 4.1 QP Optimality Conditions -- 4.2 QP Duality -- 4.3 Unique and Alternate Optimal Solutions -- 4.4 Sensitivity Analysis -- 4.5 Exercises -- 5 QP Solution Algorithms -- 5.1 A Basic QP Algorithm: Algorithm 3 -- 5.2 Determination of an Initial Feasible Point -- 5.3 An Efficient QP Algorithm: Algorithm 4 -- 5.4 Degeneracy and Its Resolution -- 5.5 Computer Programs -- 5.6 Exercises -- 6 A Dual QP Algorithm -- 6.1 Algorithm 5 -- 6.2 Computer Programs -- 6.3 Exercises -- 7 General QP and Parametric QP Algorithms -- 7.1 A General QP Algorithm: Algorithm 6 -- 7.2 A General PQP Algorithm: Algorithm 7 -- 7.3 Symmetric Matrix Updates -- 7.4 Computer Programs -- 7.5 Exercises -- 8 Simplex Method for QP and PQP -- 8.1 Simplex Method for QP: Algorithm 8 -- 8.2 Simplex Method for PQP: Algorithm 9 -- 8.3 Computer Programs -- 8.4 Exercises -- 9 Nonconvex Quadratic Programming -- 9.1 Optimality Conditions -- 9.2 Finding a Strong Local Min: Algorithm 10 -- 9.3 Computer Programs -- 9.4 Exercises -- Bibliography -- Index "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."--Provided by publisher