A general data-driven nonlinear robust optimization framework based on statistic limit and principal component analysis

Abstract

A general robust optimization framework is proposed to solve nonlinear programming under uncertainty. A compact convex data-driven uncertainty set is first conducted by leveraging the combined index statistic limit technique. It can effectively capture the correlations among uncertain variables by using the principal component analysis model, and eliminate the noise in massive uncertainty data. Based on the proposed uncertainty set, linearization is taken to approximate nonlinear optimization with inequality-only constraints by using first-order Taylor approximation. By using the implicit function theorem, it is extended to a general formulation involving both inequality and equality constraints. Due to the potential limitation of first-order Taylor approximation, an iterative algorithm is designed to realize multiple linearization to search for a global robust solution under large perturbation. The efficiency of the proposed approach is verified on simulated numerical experiences, and the proposed method is applied to the industrial process of gold cyanidation leaching.