Abstract

Many problems in science and engineering can be formulated as nonlinear
optimization problems in which the goal is to find an acceptable input
vector *x* that minimizes the value of a scalar objective
function
*f(x)*.
Although many numerical algorithms for solving such problems have been
extensively analyzed, surprisingly few achieve satisfactory performance
when the objective is defined by expensive computer simulations of
complex physical processes. Such objective functions pose peculiar
challenges that must be addressed in new ways; accordingly, we will
discuss the development of algorithms for numerical optimization in this
environment that are computationally tractable and analytically sound.