C. Audet and J. E. Dennis Jr., “Mesh Adaptive Direct Search Algorithms for Constrained Optimization,” SIAM Journal on Optimization, Vol. 17, No. 1, 2006, pp. 188-217. doi:10.1137/040603371

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.