Research On The Relative Robust Conditional Value-at-risk And The Distributionally Robust Optimization

As an optimization method to deal with data uncertainty,robust optimiza-tion has become a hot spot in the field of optimization.In this field,the research on relative robust optimization and distributionally robust optimization have been concerned by many experts.In this paper,we mainly discuss the problem of relative robust conditional value-at-risk optimization with mixture distribution and the distributionally robust optimization under probabilistic envelope constraints.For the first problem,we first propose the definition of relative robust conditional value-at-risk under mixture distribution and discuss its properties.Then the approximate transformation of the value-at-risk problem is given.Finally,a numerical experiment is carried out under the assumption that the distribution is normal distribution,and the investment portfolio problem is taken as an example.The results show that the above method can effectively solve the portfolio problem.For the second problem,its objective function is assumed to be a linear function,and the constraint condition contains the probabilistic envelope constraints.Firstly,the original problem is transformed into the max-min optimization problem by dealing with the probabilistic envelope constraints.Then it is transformed into a semidefinite programming problem by alternating optimization.Finally,a numerical experiment is carried out on the dynamic water tank problem.The results show that the proposed method can effectively deal with the problem of dynamic water tank.Finally,we make a brief summary and prospect for this paper.