Solving Two-stage Quadratic Multiobjective Problems via Optimality and Relaxations
研究了鲁棒两阶段二次多目标优化问题，提出了新的最优性条件（用线性矩阵不等式表示）和松弛方案，通过半定规划或二阶锥规划寻找有效解，并给出数值示例验证。
Abstract This paper focuses on the study of robust two-stage quadratic multiobjective optimization problems. We formulate new necessary and sufficient optimality conditions for a robust two-stage multiobjective optimization problem. The obtained optimality conditions are presented by means of linear matrix inequalities and thus they can be numerically validated by using a semidefinite programming problem. The proposed optimality conditions can be elaborated further as second-order conic expressions for robust two-stage quadratic multiobjective optimization problems with separable functions and ellipsoidal uncertainty sets. We also propose relaxation schemes for finding a (weak) efficient solution of the robust two-stage multiobjective problem by employing associated semidefinite programming or second-order cone programming relaxations. Moreover, numerical examples are given to demonstrate the solution variety of our flexible models and the numerical verifiability of the proposed schemes.