Course Description
An introduction to optimization theory and various methods to formulate and solve optimization problems. Those include simplex methods to solve linear programs, quadratic programming, and nonlinear programming. The course will also examine several engineering applications of the optimization methods covered in the course.
Athena Title
Optim Theory and Engr Applicat
Prerequisite
MATH 2700
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
This graduate-level course first introduces foundations for optimization models and presenting constraints. Linear and nonlinear optimization will then be discussed, and the methods to solve them for both constrained and unconstrained optimization will be covered. Numerous applications are presented in electrical (control), civil, and mechanical engineering. The objective is to maintain a balance between theory and problem setup for solution using standard optimization software tools (such as MATLAB) with applications to engineering systems. Upon successful completion of this course, the students will be able to understand: (1) basic theoretical principles in optimization; (2) formulation of optimization models; (3) solution methods in optimization; (4) methods of sensitivity analysis and post processing of results; (5) applications to a range of engineering problems.
Topical Outline
1. An introduction to optimization models, linear and nonlinear optimization 2. Feasibility, optimality, and convexity in optimization problems 3. General optimization algorithms and Newton’s method for nonlinear equations 4. Representation of linear constraints 5. Geometry of linear programming: standard form, basic solutions, and optimality 6. Simplex method to solve linear optimization problems 7. Duality and sensitivity 8. Network problems: introduction and basic concepts 9. Basics of unconstrained optimization: optimality conditions, Newton’s method, line search methods 10. Optimality conditions for constrained problems: linear constraints case 11. Lagrange multipliers and the Lagrangian function 12. Optimality conditions for constrained problems: nonlinear constraints case 13. Various applications of optimization in engineering problems
Syllabus
Public CV