Design Theory and Methods using CAD/CAE

3.5. Gradient-Based Approach

The gradient-based approach solves optimization problems by searching in the design space based on the gradients of objective and constraint functions that are active using numerical algorithms. This approach solves for both constrained and unconstrained problems of more than two design variables. However, for illustration purposes, we use examples of one or two design variables.

The gradient-based approach starts with an initial design. This approach searches for a local minimum that is closest to the initial design in an iterative manner. Note that for constrained problems, if the initial design is infeasible, the goal of the search is often to first bring the design into the feasible region. In doing so, the objective ...