21.4.5. Numerical Optimization Algorithm

Let’s consider the general constrained optimization problem as

Minimize \(f\left( \mathbf{x} \right)\)

Subject to

\({{h}_{i}}\left( \mathbf{x} \right)=0,\text{ }i=1,2,...,l\)

\({{g}_{j}}\left( \mathbf{x} \right)\le 0,\text{ }j=1,2,...,m\)

\(\mathbf{x}\in \Omega\)

where, \(l\le n\) and functions \(f\), \({{h}_{i}}\) and \({{g}_{j}}\) are continuous and their second derivatives are continuous. In general, the function we call \(f\) be objective, \({{h}_{i}}\) be equality constraints and \({{g}_{j}}\) be inequality constraints.

RecurDyn/AutoDesign uses the augmented Lagrange multiplier (ALM) method to solve the approximate optimization problem. Next, we explains the basic concept of ALM.

• 21.4.5.1. Augmented Lagrange Multiplier Method
• 21.4.5.2. Multi-Objective Optimization
• 21.4.5.3. Robust Design Optimization & DFSS