Large Scale Optimization Using Multipoint Cubic Approximation

Abstract

This paper presents a generalized algorithm to optimize nonlinear, constrained problems with complex or computationally expensive functions and a large number of design variables. A multipoint cubic approximation method that relies on a reduced design space of previous points is used within the optimization routine. This approximation method signi…cantly reduces the size of the Hessian matrix. Also, by providing a higher-order approximation, it reduces the number of exact objective and constraint function calculations required. In addition, a quadratic programming routine provided by MOSEK ApS is used to solve the quadratic subproblem for the large number of design variables. A scalable cantilever beam is used to verify the algorithm. Results demonstrate that as the number of design variables increases, the number of iterations required to converge to an optimum solution does not dramatically increase.