Engineering optimization
Graduate · Engineering
Syllabus focus
Standard syllabus · STEM / applied
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
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
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.