The optimization algorithm bundled with Sculptor is called the Generalized Reduced Gradient (GRG) algorithm. It is a gradient-based algorithm. It finds a gradient to determine the search direction. The GRG algorithm is designed to always provide a feasible solution (one that does not violate any of the constraints). If the initial design is not a feasible solution, GRG tries to move into feasible design space (find a feasible solution) first. The GRG algorithm determines a search direction by taking the gradient of the objective function numerically. To do this, it performs an analysis of the unperturbed design. Then, it numerically perturbs each design variable and runs another analysis. The gradient is determined numerically from either a forward or central difference.
After the GRG algorithm obtains a full gradient (the gradient is a vector of length n where n is the number of design variables), to define the search direction, it will do a one-dimensional line search for the minimum (maximum) in that direction. Initially, a small step is taken in the search direction, set by the Initial value. The step length will increase with each step, while looking for a minimum. After it passes the minimum, a quadratic curve is fitted to obtain a close value for the minimum.