The chapter discusses the role of optimization in design, the types of optimization problems, and the difference between acceptable and optimal design solutions. The chapter shows how an optimal design problem can be set (including the explanation of simple and compound measures of merit, variables, and limitations). In particular, the chapter discusses Lagrange multipliers method, linear and integer programming, descent methods (including the gradient descent method and the method of the fastest descent), the Newton–Raphson method, and random search methods.