Feb 01, 2023  
2021-2022 Undergraduate Academic Catalog 
2021-2022 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 344 - Nonlinear Programming

3 lecture hours 0 lab hours 3 credits
Course Description
This course introduces the fundamentals of nonlinear optimization. Topics include convex sets and functions, necessary and sufficient optimality conditions, duality in convex optimization, and algorithms for unconstrained and constrained optimization problems. (prereq: MA 343 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Understand the differences between linear, integer and nonlinear programs, as well as their levels of computational complexities
  • Learn the basic properties of convex sets and functions and common operations that preserve convexity
  • Solve small constrained and unconstrained convex nonlinear programs by hand
  • Understand and be able to verify the Karush-Kuhn-Tucker optimality conditions
  • Understand the Lagrangian function, and the notion of duality in convex optimization

Prerequisites by Topic
  • The basic principles of algebra
  • Differentiation of algebraic functions
  • Exposure to multivariate calculus and partial derivatives
  • Experience with formulating industrial and graph theoretical problems using integer and linear programs
  • Duality theory in linear programming
  • Exposure to vectors and matrices

Course Topics
  • Introduction to nonlinear programs
  • Convex sets and functions
  • Karush-Kuhn-Tucker conditions, gradient version
  • Lagrangian duality
  • Algorithms for unconstrained optimization
  • Algorithms for constrained optimization

Edward Griggs

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