# Syllabus Math 484

## Math 484. Nonlinear Programming Instructor Syllabus

Text: A. Peressini, F. E. Sullivan, and J. J. Uhl, The Mathematics of Nonlinear Programming, Springer-Verlag, 1993.

Chapter 1 - Unconstrained Optimization via Calculus (4 lectures)

• Introductory Remarks and 1.1 Functions of One Variable (1)
• 1.2 Functions of Several Variables (1)
• 1.3 Positive and Negative Definite Matrices and Optimization (1)
• 1.4 Coercive Functions and Global Minimizers and 1.5 Eigenvalues of Positive Definite Matrices (1)

Chapter 2 - Convex Sets and Convex Functions (8 lectures)

• 2.1 Convex Sets (1)
• 2.3 Convex Functions (3)
• 2.4 Convexity and the Arithmetic - Geometric Mean Inequality) (2)
• 2.5 Unconstrained Geometric Programming (2)

Chapter 3 - Iterative Methods for Unconstrained Optimization (10 lectures)

• 3.1 Newton's Method (3)
• 3.2 The Method of Steepest Descent (2)
• 3.3 Beyond Steepest Descent (2.)
• 3.4 Broyden's Method (2)
• 3.5 Secant Methods for Mininization (1)

Chapter 4 - Least Squares Optimization (4 lectures)

• 4.1 Least Squares Fit (1)
• 4.2 Subspaces and Projections (1)
• 4.3 Minimum Norm Solutions of Underdetermined Linear Systems (1)
• 4.4 Generalized Inner Products and Norms: The Portfolio Problem (1)

Chapter 5 - Convex Programming; Karush-Kuhn-Tucker Theorem (6 lectures)

• 5.1 Separation and Support Theorems for Convex Sets (2)
• 5.2 Convex Programming: The Karush-Kuhn-Tucker Theorem (3)
• 5.3 Constrained Geometric Programming (1)

Chapter 6 - Penalty Methods (3 lectures)

• 6.1 Penalty Functions (1)
• 6.2 The Penalty Method (1)
• 6.3 Applications of the Penalty Method to Convex Programs (1)

Chapter 7 - Optimization with Equality Constraints (2 lectures)

• 7.1 Surfaces and Their Tangent Planes (1)

Leeway and Test Periods (6 lectures)

Total: 43