G. W. Wasilkowsi and H. Wozniakowski, “Explicit Cost Bounds of Algorithms for Multivariate Tensor Product problems,” Journal of Complexity, Vol. 11, No. 1, 1995, pp. 1-56. doi:10.1006/jcom.1995.1001

has been cited by the following article:

• 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.