Introduction

• A problem statement is the concise description of an optimization task:

$$\begin{aligned} \min_{\boldsymbol{x}} \quad & f(\boldsymbol{x}) \\ \text{subject to} \quad & \boldsymbol{h}(\boldsymbol{x}) = \mathbf{0} \\ & \boldsymbol{g}(\boldsymbol{x}) \leq \mathbf{0} \\ & \boldsymbol{x}_l \leq \boldsymbol{x} \leq \boldsymbol{x}_u \end{aligned}$$

• $\boldsymbol{x}$ : vector of design variables
• $f(\boldsymbol{x})$ : objective function
• $\boldsymbol{h}(\boldsymbol{x})$ : equality constraint functions
• $\boldsymbol{g}(\boldsymbol{x})$ : inequality constraint functions
• $\boldsymbol{x}_l, \boldsymbol{x}_u$ : lower and upper bounds, define design space

MDO