TITLE:
A Derivative-Free Optimization Algorithm Using Sparse Grid Integration
AUTHORS:
Shengyuan Chen, Xiaogang Wang
KEYWORDS:
Nonlinear Programming; Derivative Free Optimization; Sparse Grid Numerical Integration; Conditional Moment
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.3 No.1,
March
27,
2013
ABSTRACT: We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and evaluating its value is also very expensive. The new algorithm has: 1) a unique starting point strategy; 2) an effective global search heuristic; and 3) consistent local convergence. These are achieved through a uniform use of sparse grid numerical integration. Numerical experiment result indicates that the algorithm is accurate and efficient, and benchmarks favourably against several state-of-art derivative free algorithms.