Abstract: This paper presents an equivalent solvable model for a two-stage distributionally robust optimization (DRO) framework with Conditional Value-at-Risk (CVaR).Under the condition of incomplete information regarding the distribution of random variables,an ambiguity set is constructed using the second-order moment information to establish the two-stage DRO-CVaR model.When the coefficients of the second-stage objective function are random variables,the model is transformed into a directly solvable semidefinite programming (SDP) problem by leveraging conic duality theory and the minimax principle.

Key words: onditional value-at-risk, distributionally robust optimization, duality theory, semidefinite programming