Solution Of A Class Of Nonlinear Distributionally Robust Chance Constrain Problems

The chance constrained programming is a stochastic programming problem that solves the optimal value under certain probability constraints, it refers to the inclu-sion of random variables in constraints that must be made before the observed values of the random variables are fulfilled problem. A common way to solve the chance con?strained problem is to transformed it into a convex constraint that is easy to solve.This convex constraint is called a safety approximation of opportunity constraint optimization.Because chance constraint can be more accurately portrayed.Real life has the uncertainty of the influencing factors, so in the financial, water conservancy and electric power, transportation and other sectors of the wind,risk management and control issues have a wide range of applications.In this paper, we mainly consid-er the theory research and the algorithm exploration of the distributionally robust optimization problem under the chance constraint.First,we summarized several approximate methods for independent chance con-straints and joint chance constraints in the case of random variable distribution information incomplete(distributed robust chance constrained).The WC-CVaR ap-proximation of the independent chance constraint is that the constraint function is transformed into a desired form by the CVaR approximation.Then,the dual theory is used to transform it into deterministic and easy to solve convex constraints;The bonferroni approximation of joint chance constrained mainly transforms the orig-inal constraints through Bonferroni inequality, and the joint chance constraint is decomposed into m individual chance constraints.Chen[40]et al used the inequality of probability theory transformed the chance constrained problem into a second-order cone constraint problem.Yang[42]et al.studied the robust optimization of random variables in the case of convex quadrati cconditions,and transformed the problem into semidefinite constraint problem.Second,based on the study of chance constraints of Zylmer[40]et al,we studied the distributionally robust chance constrained problem with random variables and decision variables is quadratic.The problem is approximated by the WC-CVaR ap-proximation method.the nonlinear matrix inequalities(NLMIs) is transformed into a linear matrix inequalities(LMIs)by the relaxation method.The effectiveness of the proposed method is verified by numerical experiments.