Research On Globalized Distributionally Robust Conic Optimization Based On Moment Information

Due to the existence of uncertainty,classical optimization models are often biased against the real situation in life.Even small data perturbations may have a large impact on the model,such as the solution we obtain does not satisfy the constraint conditions or it is not the optimal solution at all.However,distributionally robust optimization(DRO)can effectively reduce the influence of the uncertainty of parameter.DRO selects the worst case in the uncertainty set containing all possible distributions as the optimal case.Therefore the solution of DRO is too conservation.To solve this problem,we proposes a globalized distributionally robust conic optimization(GDRCO).We first study GDRCO with the penalty term in the uncertainty set,in which the constraint of the distance function between variables is added to allow the model having a certain degree of variable distribution which is not in the sample estimation support set,to reduce the conservatism.The transformation results of GDRCO are applied to the models in which uncertainty set is contained with moment,Mahalanobis distance,coefficient of variation or mean absolute deviation constraints,then the tractable forms are obtained,respectively.Furthermore,we consider another kind of GDRCO with the penalty term on the objective function.Similarly,we obtain the tractable globalized distributionally robust conic counterpart under four different constraints.The global nature of the model in this dissertation can reduce the conservatism of DRO.The conic constraint in the uncertainty set has generality so the models can be applied to different specific situations and obtain tractable forms.