Research On A Class Of Distributed Robust Optimization Problems With Linear Form

In this paper,we study the solution of a class of distributed robust optimization problems with linear form based on ?~2-divergence measure.The model studied is as follows min (?) Where,(?)In this paper,the uncertainty set ? is defined according to the ?~2-divergence,under the premise that the empirical distribution is known,the distribution set is defined by the distribution that does not exceed an integer from the empirical distribution.According to the X2-divergence theory,measure conversion,and duality theory,the distribution robust optimization problem with unknown distribution is equivalent to the distribution robust optimization problem under the empirical distribution p0.First,the empirical distribution is obtained from historical data.Considering the ?~2-divergence distance between empirical distribution p0 and unknown distribution p,an uncertain set of distribution p is constructed.Secondly,using the concept of likelihood ratio and measure conversion,the equivalent conversion between the original distribution problem and the distribution problem is realized,and the constraint problem in the above distribution optimization model is transformed into a convex second-order cone constraint.Finally,through a series of equivalent conversions,a distribution robust portfolio optimization model equivalent to the original problem is obtained.The first part of the article introduces the research background and current status of distributed robust optimization problems,and the distribution robust optimization theory and basic concepts.In the second part,we study a class of linear distribution robust optimization problems.Based on divergence theory,measure conversion and convex optimization theory,the equivalent form of the original problem is solved.The third part introduces the solution process of the equivalent form of distributionally robust investment portfolio optimization problems.