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IEMS 314: Nonlinear Optimization for Decision Making


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Prerequisites

GEN_ENG 150 or COMP_SCI 150 GEN_ENG 231 GEN_ENG 241 MATH 228-1; or equivalent

Description

This course studies the formulation and solution of nonlinear optimization models arising in AI,
finance, and engineering design. Methods include gradient, stochastic gradient, and Newton
methods. Modeling and solution are carried out in Python.

LEARNING OBJECTIVES
  • Students will understand and be able to formulate nonlinear optimization models, both deterministic and stochastic.
  • Students will know optimality conditions for both unconstrained and constrained problems.
  • Students will understand how machine learning systems are trained, how to optimize financial portfolios, and how to solve engineering design problems.
  • Students will be able to apply several fundamental optimization algorithms.
  • Students will know how to evaluate solutions to optimization problems.
  • Students will be able to use software to model and solve nonlinear optimization problems.
TOPICS
  • Nonlinear optimization models in engineering
  • The gradient method
  • Automatic differentiation (backpropagation)
  • The stochastic gradient method
  • Newton, quasi-Newton, and Gauss–Newton methods
  • Optimality conditions for constrained problems
  • Introduction to methods for constrained optimization
  • Case studies in AI, finance, and engineering design
MATERIALS
Reference:

Jorge Nocedal and Stephen J. Wright. Numerical Optimization, 2nd edition. Springer Series in Operations Research and Financial Engineering. Springer, New York, 2006. ISBN 978-0-387-30303-1.

ADDITIONAL INFORMATION

Introduction to nonlinear optimization, including gradient methods and automatic differentiation. Training of AI systems using stochastic gradient methods. Newton and Newton-like methods for structured or large-scale problems. Optimality conditions for constrained optimization. Case studies in finance and engineering design. Formulation and solution using Python. Students work in teams on a project involving the direct application of concepts learned in the course.

CATALOG DESCRIPTION

Theory and algorithms of nonlinear optimization as a bridge between deterministic linear models and datadriven decision making under uncertainty. This course covers convex and nonconvex modeling, first and secondorder optimality conditions, duality theory, and numerical methods including gradientbased, stochastic, Newtontype, and constrained optimization algorithms. Case studies from machine learning, finance, and engineering motivate the formulation and analysis of realworld nonlinear models. Students implement foundational solvers from first principles, construct more advanced solvers using generativeAI–assisted development, and deploy these methods on applications such as nonlinear regression and classification, portfolio optimization, and parameter estimation in complex systems.

Syllabus