摘要
Linear programming models have been widely used in input-output analysis for analyzing the interdependence of industries in economics and in environmental science.In these applications,some of the entries of the coefficient matrix cannot be measured physically or there exists sampling errors.However,the coefficient matrix can often be low-rank.We characterize the robust counterpart of these types of linear programming problems with uncertainty set described by the nuclear norm.Simulations for the input-output analysis show that the new paradigm can be helpful.
Linear programming models have been widely used in input-output analysis for analyzing the interdependence of industries in economics and in environmental science.In these applications,some of the entries of the coefficient matrix cannot be measured physically or there exists sampling errors.However,the coefficient matrix can often be low-rank.We characterize the robust counterpart of these types of linear programming problems with uncertainty set described by the nuclear norm.Simulations for the input-output analysis show that the new paradigm can be helpful.
基金
supported by National Social Science Foundation of China (Grant No. 11BGL053)
National Natural Science Foundation of China (Grant Nos. 11101434,10971122 and 11101274)
Scientific and Technological Projects of Shandong Province (Grant No. 2009GG10001012)
Excellent Young Scientist Foundation of Shandong Province (Grant No. 2010BSE06047)
the Doctoral Program of Higher Education of China (Grant No. 20110073120069)
Shandong Province Natural Science Foundation (Grant No. ZR2012GQ004)
Independent Innovation Foundation of Shandong University (Grant No. 12120083399170)
