High-accuracy non-gradient optimiser by vectorised iterative discrete approximation and single-GPU computing

摘要

High-accuracy optimiser is the success of resolution-sensitive applications such as computational finance and scientific computing. However, if the cost function is complicated with a large number of peaks, it is computationally expensive for the optimiser to reach high-accuracy and to satisfy the needs of these applications. In this paper, by the novel idea of single-GPU-based iterative discrete approximation, we develop a high-accuracy non-gradient optimiser, iterative discrete approximation Monte Carlo search (single-GPU IDA-MCS), with the style of single instruction multiple data by CUDA 5.0, and we illustrate the performance of the algorithm by finding the optimum of a cost function up to hundreds of peaks. Computational results show that the accuracy of optima from a single-GPU IDA-MCS with ten iterations and 104 elements is significantly higher than the conventional method Monte Carlo search with 1,000 iterations and 108 elements. Computational results also show that, by the same number of iterations and elements, the accuracy of a single-GPU IDA-MCS is higher than (weighted) discrete approximation Monte Carlo search.