Engineering optimization
Graduate · Engineering
Syllabus focus
Topics typically covered
Standard syllabus
Linear and nonlinear programming
- Optimization problem formulation and convexity
- Linear programming: simplex method and duality
- Sensitivity analysis and shadow prices
- Integer programming and branch-and-bound
- Unconstrained nonlinear optimization algorithms
- Gradient descent, Newton, and quasi-Newton methods
- Constrained optimization: KKT conditions
- Penalty and barrier methods
- Sequential quadratic programming (SQP)
- Global optimization heuristics overview
Specialized engineering formulations
- Least squares and regression as optimization
- Multi-objective optimization and Pareto fronts
- Dynamic programming and optimal control link
- Stochastic programming and chance constraints intro
- Robust optimization under uncertainty
- Topology optimization SIMP method
- Shape optimization and adjoint methods
- Scheduling and network flow problems
- Engineering design optimization case studies
- Convex relaxations for nonconvex problems
STEM / applied
Computation and software
- MATLAB Optimization Toolbox and CVX
- Python: SciPy, PuLP, and Pyomo
- GAMS and AMPL modeling languages survey
- Large-scale solvers: IPOPT, Gurobi licensing
- Parallel and decomposition methods
- Simulation-based optimization and surrogate models
- Machine learning hyperparameter tuning as optimization
- Real-time optimization in process control
- Benchmark problems and reproducibility
- Thesis optimization model development
Applications across disciplines
- Structural weight minimization with constraints
- Aerospace vehicle trajectory optimization
- Supply chain and logistics network design
- Energy unit commitment problems
- Parameter estimation in biochemical models
- Portfolio optimization analogies in engineering risk
- Autonomous vehicle path planning objectives
- Multi-disciplinary design optimization (MDO)
- Industry guest cases from operations research
- Qualifying exam optimization preparation
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Linear and nonlinear programming
Optimization problem formulation and convexity
Coming soon - Specialized engineering formulations
Least squares and regression as optimization
Coming soon - Computation and software
MATLAB Optimization Toolbox and CVX
Coming soon - Applications across disciplines
Structural weight minimization with constraints
Coming soon
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.