**ChE488/EID488: Convex Optimization Techniques**

## Prof. Davis

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*Course Syllabus*

*Course Description:*

This course discusses in detail the methods for setting up and solving optimization problems of engineering and economic interest using the techniques of unconstrained, linear, and nonlinear programming. An eventual goal of the course is to give students enough context to understand convex optimization, which is the solution of problems with only global minima or maxima (one answer). The course is centered around a project assignment, where students will pose, set up, and solve a problem of their choice. We will consider example problems (supply chain management, network flow, portfolio optimization, etc.) across engineering disciplines. The focus will be on theory and problem formulation, with some computational component. The first half of the course (before the Midterm Exam) will cover:

- Introduction to optimization and motivating problems

- Methods of proof and notation (Ch. 1 of Chong and Zak)

- Matrices, Matrix properties, Norms (Ch. 2 and 3)

- Geometry of typical sets from optimization problems (Ch. 4)

- Review of multivariable calculus (Ch. 5)

- Unconstrained optimization (Ch. 6)

The second half of the course (from the Midterm to the Final Exam) will cover:

- Algorithms and solution methods for unconstrained problems (Ch. 7-14)

- Linear programming problems (Ch. 15)

- Solution methods for linear and integer programming problems (Ch. 16 and Ch. 19)

- Duality in LPs and examples of linear programs (Ch. 17)

- Nonlinear constrained programming problems and their optimality conditions (Ch. 20-21)

- Convexity and convex optimization problems (Ch. 22)

*Example Student Projects:*

*Example 1*

*Example 2*