The Mathematics of Nonlinear Programming

Cover......Page __p_0000.djvu
Copyright......Page __p_0004.djvu
Contents......Page __p_0009.djvu
Preface......Page __p_0005.djvu
1.1. Functions of One Variable......Page __p_0011.djvu
1.2. Functions of Several Variables......Page __p_0015.djvu
1.3. Positive and Negative Definite Matrices and Optimization......Page __p_0023.djvu
1.4. Coercive Functions and Global Minimizers......Page __p_0035.djvu
1.5. Eigenvalues and Positive Definite Matrices......Page __p_0039.djvu
Exercises......Page __p_0041.djvu
2.1. Convex Sets......Page __p_0047.djvu
*2.2. Some Illustrations of Convex Sets in Economics -- Linear Production Models......Page __p_0053.djvu
2.3. Convex Functions......Page __p_0055.djvu
2.4. Convexity and the Arithmetic-Geometric Mean Inequality -- An Introduction to Geometric Programming......Page __p_0068.djvu
2.5. Unconstrained Geometric Programming......Page __p_0076.djvu
*2.6. Convexity and Other Inequalities......Page __p_0083.djvu
Exercises......Page __p_0087.djvu
3. Iterative Methods for Unconstrained Optimization......Page __p_0092.djvu
3.1. Newton\'s Method......Page __p_0093.djvu
3.2. The Method of Steepest Descent......Page __p_0107.djvu
3.3. Beyond Steepest Descent......Page __p_0115.djvu
3.4. Broyden\'s Method......Page __p_0122.djvu
3.5. Secant Methods for Minimization......Page __p_0131.djvu
Exercises......Page __p_0138.djvu
4.1. Least Squares Fit......Page __p_0143.djvu
4.2. Subspaces and Projections......Page __p_0151.djvu
4.3. Minimum Norm Solutions of Underdetermined Linear Systems......Page __p_0155.djvu
4.4. Generalized Inner Products and Norms; The Portfolio Problem......Page __p_0158.djvu
Exercises......Page __p_0162.djvu
5. Convex Programming and the Karush-Kuhn-Tucker Conditions......Page __p_0166.djvu
5.1. Separation and Support Theorems for Convex Sets......Page __p_0167.djvu
5.2. Convex Programming; The Karush-Kuhn-Tucker Theorem......Page __p_0179.djvu
5.3. The Karush-Kuhn-Tucker Theorem and Constrained Geometric Programming......Page __p_0198.djvu
5.4. Dual Convex Programs......Page __p_0209.djvu
*5.5. Trust Regions......Page __p_0220.djvu
Exercises......Page __p_0222.djvu
6.1. Penalty Functions......Page __p_0225.djvu
6.2. The Penalty Method......Page __p_0229.djvu
6.3. Applications of the Penalty Function Method to Convex Programs......Page __p_0236.djvu
Exercises......Page __p_0245.djvu
7. Optimization with Equality Constraints......Page __p_0248.djvu
7.1. Surfaces and Their Tangent Planes......Page __p_0250.djvu
7.2. Lagrange Multipliers and the Karush-Kuhn-Tucker Theorem for Mixed Constraints......Page __p_0255.djvu
7.3. Quadratic Programming......Page __p_0268.djvu
Exercises......Page __p_0276.djvu
Index......Page __p_0281.djvu