01 | Module
Formulating an Optimization Problem
Design variables, objective functions, constraints, and the feasible region.
Start module →Course 24 | Advanced Engineering Methods
Optimization for Mechanical Engineers
Use design variables, constraints, objective functions, sensitivity, trade-offs, and optimization methods to improve engineering designs.
Course snapshot
- Purpose
- Optimization teaches how to choose better designs under constraints instead of only analyzing one design at a time.
- Used in Career directions
- Content status
- Lesson hub
How to study this course
- Define the design variables
- State the objective and constraints
- Choose the evaluation model
- Run or reason through alternatives
- Check sensitivity and trade-offs
- Recommend a design with limits
01
How this course is designed
Formulate before you solve
Half of optimization is stating the problem: naming the design variables, the objective, and the constraints. A clean formulation makes the method almost mechanical; a sloppy one cannot be rescued by any solver.
Unconstrained, then constrained
The first five modules master the unconstrained core: optimality conditions and the descent methods that find a minimum. The last five add constraints, the KKT conditions, programming, and the trade-offs of real design.
Worked numbers throughout
Every module includes two fully worked examples with verified arithmetic, each ending in an answer you can certify with an optimality condition, not just a number a solver returned.
02
The 10 modules
02 | Module
Unconstrained Optimality Conditions
The gradient, the Hessian, and the first and second-order conditions.
Start module →03 | Module
Line Search and Steepest Descent
Descent directions, step length, and the sufficient-decrease condition.
Start module →04 | Module
Newton and Quasi-Newton Methods
The Newton step, quadratic convergence, and the BFGS idea.
Start module →05 | Module
Nonlinear Least Squares
The least-squares objective, Gauss-Newton, and Levenberg-Marquardt.
Start module →06 | Module
Constrained Optimization and the KKT Conditions
Lagrange multipliers, the KKT conditions, and active constraints.
Start module →07 | Module
Linear Programming
The feasible polygon, vertices, and the simplex idea.
Start module →08 | Module
Quadratic Programming and Penalty Methods
The KKT system for a QP and penalty and barrier reformulations.
Start module →09 | Module
Derivative-Free and Global Optimization
Golden-section search, the Nelder-Mead simplex, and global methods.
Start module →10 | Module
Multi-Objective and Design Optimization
Weighted sums, Pareto fronts, and engineering trade-offs.
Start module →