MAE 598/494 Design Optimization | Fall 2017

Faculty: Max Yi Ren


Office: GWC464

Location & Time: ECAA219, TU/TH 4:30pm-5:45pm

Office hours: TU/TH 2:00pm-4:00pm in GWC464, or by appointment

Prerequisites: No previous knowledge about optimization is expected or required. However, solid background in calculus and linear algebra is assumed ([Math review][mathreview]). Students are also expected to have basic programming skills (Matlab and Python preferred).

Course Overview

The purpose of this course is to introduce the student to mathematical modeling, optimization theory, and computational methods for analytical and simulation-based optimal system design. The student will learn to (i) develop proper mathematical models to formulate design optimization problems and (ii) develop and apply appropriate optimization algorithms to solve them.

Workload and grading

There are 5 homework assignments, 2 mid-term exams, and an individual project.

Course schedule

Date Topic Assignment Note
Aug 17 (TH) Introduction to optimization HW 1 in  
Aug 22 (TU) Math review 1: Linear algebra and matrix calculus    
Aug 24 (TH) Unconstrained optimization 1: Convexity and optimality conditions HW 1 due, HW 2 in  
Aug 29 (TU) Unconstrained optimization 2: Gradient descent and convergence    
Aug 31 (TH) Unconstrained optimization 3: Modern line search techniques    
Sep 5 (TU) Unconstrained optimization 4: Newton’s method    
Sep 7 (TH) Unconstrained optimization 5: Application - Origami design HW 2 due  
Sep 12 (TU) Unconstrained optimization 6: Trust Region    
Sep 14 (TH) Mid-term 1    
Sep 19 (TU) Math review 2: Random variables and probability distributions HW 3 in  
Sep 21 (TH) Metamodeling 1: Ordinary least square, Regularization, Information criteria   Max out of town
Sep 26 (TU) Metamodeling 2: Design of experiments    
Sep 28 (TH) Metamodeling 3: Neural networks    
Oct 3 (TU) Metamodeling 4: Gaussian process    
Oct 5 (TH) Metamodeling 5: Application - Efficient global optimization HW 3 due  
Oct 10 (TU) Full break    
Oct 12 (TH) Constrained optimization 1: Reduced gradient HW 4 in  
Oct 17 (TU) Constrained optimization 2: KKT conditions    
Oct 19 (TH) Constrained optimization 3: KKT geometry, sensitivity analysis    
Oct 24 (TU) Constrained optimization 4: Generalized reduced gradient    
Oct 26 (TH) Constrained optimization 5: Application - Topology optimization    
Oct 31 (TU) Constrained optimization 7: Quasi-Newton methods HW 4 due, HW 5 in  
Nov 2 (TH) Constrained optimization 8: Active set strategy    
Nov 7 (TU) Constrained optimization 9: Sequential Quadratic Programming    
Nov 9 (TH) Mid-term 2    
Nov 14 (TU) Constrained optimization 10: Duality HW 5 due  
Nov 16 (TH) Math review 3: Markov decision process    
Nov 21 (TU) Optimal control 1: Model-free methods    
Nov 23 (TH) Thanksgiving    
Nov 28 (TU) Optimal control 2: Model-based methods    
Nov 30 (TH) Optimal control 3: Evolutionary strategies    


The course project for this year will be on robot topology, sensor, and controller design through evolution and policy search. Details TBD.

Academic Integrity

Each student has an obligation to act with honesty and integrity, and to respect the rights of others in carrying out all academic assignments. MAE 540 will follow the process defined by the Office of the Dean of Students, which states that any student who is found to have violated the Student Code of Conduct will, at a minimum, receive an E in the course. The College Policy defines the process to be used if the student wishes to appeal this action.