Engineering Design Optimization: Theory and Practice – Online Short Course (Starts 9 March 2026) 9 March 2026 - 8 April 2026 Online

MODULE OUTLINE:
Each module is a two-hour session that includes exercises and Q&A with the instructor.

Optimization Problem Formulation (Andrew Ning, Professor, Brigham Young University)

• Design variables, objective(s), constraints
• Classifying an optimization problem
• Using an optimizer to solve problems

Unconstrained Gradient-Based Optimization (Andrew Ning, Professor, Brigham Young University)

• Gradients, directional derivatives, Hessians
• Line Searches
• Search directions (steepest descent, conjugate gradient, Newton, Quasi-Newton, stochastic gradient descent, Adam)
• Solving unconstrained problems, understanding convergence

Constrained Gradient-Based Optimization (Andrew Ning, Professor, Brigham Young University)

• KKT conditions for equality and inequality constraints
• Penalty methods, sequential quadratic programming, interior point methods
• Solving constrained problems, understanding solver options

Derivative Computation (Christopher Lupp, Aerospace Engineer, Air Force Research Laboratory)

• Finite differencing and complex step
• Algorithmic differentiation
• Implicit differentiation (direct and adjoint methods)
• Sparse Jacobians
• Computing total derivatives for engineering problems

Derivative-Free Optimization (Ashwin Renganathan, Assistant Professor, Penn State University)

• Model-based methods (trust-region)
• Pattern and coordinate search methods
• Nelder-Mead
• Evolutionary algorithms: genetic algorithm and particle swarm
• Setting up and solving gradient-free methods

Convex Optimization (Dan Berkenstock, Science Fellow, Hoover Institution)

• Convexity
• LPs and QPs
• Geometric programming
• Setting up and solving convex optimization problems

Surrogate-Based Optimization (Nathalie Bartoli, Senior Researcher, ONERA)

• Sampling
• Surrogate construction
• Infill

Gaussian Process and Bayesian Optimization (Nathalie Bartoli, Senior Researcher, ONERA)

• Gaussian Process or Kriging
• Acquisition function (Expected Improvement criterion, etc…) for Bayesian optimization with constraints
• Extension to multi-objective Bayesian optimization

Deep Learning (Andrew Ning, Professor, Brigham Young University)

• Fundamentals of basic neural nets
• Setting up, training, and testing neural nets
• Optimization algorithms and overview of engineering architectures in deep learning

Topology Optimization (H Alicia Kim, Professor, University of California San Diego)

• Density-based and boundary-based methods.
• Setting numerical parameters and their effects on design solutions.
• Application to structural and multiphysics design problems.

Course Delivery and Materials

• The course lectures will be delivered via Zoom.
• All sessions will be available on-demand within 1-2 days of the lecture. Once available, you can stream the replay video anytime, 24/7. All slides will be available for download after each lecture.
• No part of these materials may be reproduced, distributed, or transmitted, unless for course participants. All rights reserved.
• Between lectures, the instructors will be available via email for technical questions and comments.

Dr. Andrew Ning is a professor in mechanical engineering at Brigham Young University with a joint appointment at the National Renewable Energy Laboratory. His research lab specializes in multidisciplinary optimization, deep learning, and aerodynamics as applied to wind energy and aircraft systems. He received a PhD in Aeronautics & Astronautics from Stanford University in 2011. He is co-author of the textbook Engineering Design Optimization and regularly teaches semester-length-graduate courses on optimization, deep learning, aerodynamics, and undergraduate courses on aircraft design and numerical methods.

Dr. Christopher Lupp is a Research Aerospace Engineer at the Air Force Research Laboratory (AFRL) in Dayton, Ohio. At AFRL Dr. Lupp leads several digital engineering and multi-disciplinary analysis and design optimization (MDO/MDAO/MADO) projects. His research interests include gradient-based and computationally distributed MDO, MDO including mission utility analyses, and geometrically nonlinear aeroelasticity. He received his Ph.D. from the Department of Aerospace Engineering at the University of Michigan, investigating the integration of nonlinear aeroelasticity into gradient-based MDO.

Dr. Ashwin Renganathan is an assistant professor in the department of aerospace engineering and the Institute of Computational and Data Sciences (ICDS) at Penn State. He directs the Computational complex engineered Systems Design Lab (CSDL) at Penn State, where his research focuses on developing scalable and theoretically sound mathematical and computational methods toward the design of complex engineered systems. He has designed and regularly teaches a graduate-level numerical optimization course every year at Penn State. He previously earned his Ph.D. in aerospace engineering at Georgia Tech and completed and postdoctoral appointment in applied mathematics from the Argonne National Laboratory.

Dr. Dan Berkenstock is a Science Fellow at The Hoover Institution and also a lecturer in the Department of Aeronautics and Astronautics at Stanford University. Dan’s research focuses on the application of convex, quasiconvex, & polynomial optimization methods to the design of aerodynamic shapes. His research is primarily driven by an interest in extending the breadth of known problems that can be shown to conform to these techniques. Dan received his PhD from Stanford University in 2024, working in the Aerospace Design Laboratory with Juan Alonso. He previously received an M.S. in Aeronautics and Astronautics at Stanford University and a B.S.E in Aerospace Engineering at the University of Michigan, Ann Arbor.

Nathalie Bartoli is a research director at ONERA (French Aerospace Lab in Toulouse, France) in a team dedicated to multidisciplinary optimization and conceptual aircraft design She worked on optimization algorithms within the framework of national projects or Europeans with a joint supervision of several PhDs on these subjects. She is in charge of some courses at ISAE-SUPAERO in the field of optimization and machine learning techniques.

H Alicia Kim is a professor in the Department of Structural Engineering and the Materials Science and Engineering Program at UC San Diego. Her primary research area has been in topology optimization and computational mechanics since the 90s and has published over 250 publications. Her current research focuses on coupled multiscale and multiphysics topology optimization. She has been teaching structural and topology optimization for over 15 years, to undergraduate students at the University of Bath (UK) then to graduate students at UC San Diego (USA), as well as short courses to industry.