Interval Multi-objective Optimization Problem And Its Application In Portfolio

In this thesis,we mainly discuss the multi-objective optimization problem with interval form of both objective function and constraint function.Firstly,by introducing the order relation,the interval multi-objective optimization problem is scaled,meanwhile,the relationship between the effective solution of the interval multi-objective optimization problem and the optimal solution of the weighted sum problem is explored,which expands the scaling method of the multi-objective optimization problem.Secondly,on the basis of the objective function as an interval,the KKT optimality condition of the multi-objective optimization problem that also constraints the interval is further studied,and the equivalent relation between it and the effective solution is established.Eventually,we construct the multi-objective optimization problem of interval portfolio,and give the range of weighted sum coefficients corresponding to the existence of effective portfolio.At the same time,under appropriate assumptions,we calculate the effective solution of the interval portfolio problem with a special interval form of return.In addition,we compare it with the common treatment of interval multi-objective optimization problem in the existing literature.