Text Box: Iowa State University Text Box: DEPARTMENT OF MATHEMATICS

Picture by MathWorks, demonstrating the idea of optimization.

math690v

Optimization theory and methods
Text Box: Math690v I: Constrained and Unconstrained Optimization Homework 1 Homework 2 Homework 3 Homework 4 Homework 5 Homework 6 Homework 7 Homework 8 Take-home exam 1 Take-home exam 2 Math690v II: Linear Programming, Integer and Combinatorial Optimization Homework 1 Homework 2 Homework 3 Homework 4 Homework 5 Homework 6 Homework 7 Homework 8 Take-home exam 1 Take-home exam 2

Newton’s method for nonlinear optimization
Text Box: Math690v: Optimization Theory and Methods I: Constrained and Unconstrained Optimization http://www.math.iastate.edu/wu/math690v1.html Books / References: Numerical Optimization by Jorge Nocedal and Stephen J. Wright, Practical Methods of Optimization by Roger Fletcher, Numerical Methods for Unconstrained Optimization and Nonlinear Equations by John E. Dennis, Jr. and Robert B. Schnabel Contents: Chapter 1: Introduction, Chapter 2: Fundamentals of Unconstrained Optimization, Chapter 3: Line Search Methods, Chapter 4: Trust-Region Methods, Chapter 5: Conjugate Gradient Methods, Chapter 8: Quasi-Newton Methods, Chapter 12: Theory of Constrained Optimization, *Chapter 13: Linear Programming: The Simplex Methods, *Chapter 14: Linear Programming: Interior-Point Methods, Chapter 15: Fundamental of Algorithms for Nonlinear Constrained Optimization, *Chapter 16: Quadratic Programming, Chapter 17: Penalty, Barrier, and Augmented Lagrangian Methods, Chapter 18: Sequential Quadratic Programming * — possibly be covered. Prerequisite: Minimum: multivariable calculus (math265), linear algebra (math317), Plus: advanced calculus (math414, 415), numerical analysis (math502, 503), or equivalent Course Work: Lectures (TTH), weekly homework (40%), midterm and final take-home exams (60%) Math690v: Optimization Theory and Methods II: Linear Programming, Integer and Combinatorial Optimization http://www.math.iastate.edu/wu/math690v2.html Books / References: Combinatorial Optimization by William Cook, William Cunningham, William Pulleybank, and Alexander Schrijver Contents: Linear programming: duality theory, simplex algorithm, primal-dual methods, interior point algorithms; Combinatorial optimization: shortest path problem, minimum spanning tree problem, max-flow / min-cut problem, minimum cost flow problem, maximum matching problem, traveling salesman problem, integer programming formulations, computational complexities, branch-and-bound algorithm, local search algorithm, approximation methods Prerequisite: Minimum: design and analysis of computer algorithms (coms311), graphs and networks (math314), Plus: numerical analysis (math502, math503), or equivalent Course Work: Lectures (TTH), weekly homework (40%), midterm and final take-home exams (60%)

A Traveling Salesman Problem for 666 cities in the world, solved by Groetschel, 1988.

A shortest path problem on a network of four nodes.