GRADIENT-ONLY SOLUTION STRATEGIES

Abstract

Care is usually taken during the mathematical modelling and numerical computation of the scalar function $f(\mathbf{x})$ to ensure that it is smooth and twice continuously differentiable. As highlighted in Section 6.5, the presence of numerical noise in the objective function is sometimes an unintended consequence of the complicated numerical nature frequently associated with the computation of the output function of a multi-disciplinary design optimization model. Numerical noise can also be the consequence of a deliberate computational savings strategy employed by a design engineer. This chapter is dedicated to explore alternative formulations and solution strategies when specifically dealing with piece-wise smooth discontinuous objective functions (Wilke et al. (2013b)). In essence, this chapter elaborates and formalizes the concepts and ideas introduced and hinted to in Section 6.5, that includes the handling of noisy objective functions and the use of gradient-only optimization.