In this paper, we deal with exact semidefinite programming (SDP) reformulations for a class of adjustable robust quadratic optimization problems with affine decision rules. By virtue of a special semidefinite representation of the non-negativity of separable non-convex quadratic functions on box uncertain sets, we establish an exact SDP reformulation for this adjustable robust quadratic optimization problem on spectrahedral uncertain sets. Note that the spectrahedral uncertain set contains commonly used uncertain sets, such as ellipsoids, polytopes, and boxes. As special cases, we also establish exact SDP reformulations for this adjustable robust quadratic optimization problems when the uncertain sets are ellipsoids, polytopes, and boxes, respectively. As applications, we establish the corresponding results for fractionally adjustable robust quadratic optimization problems.

在本文中，我们处理一类具有仿射决策规则的可调鲁棒二次优化问题的精确半定规划（SDP）重构。借助盒不确定集上可分离非凸二次函数的非负性的特殊半定表示，我们为谱面不确定集上的可调鲁棒二次优化问题建立了精确的SDP重构。请注意，谱面不确定集包含常用的不确定集，例如椭球体、多面体和盒子。作为特殊情况，当不确定集分别为椭球体、多面体和盒子时，我们还为这种可调鲁棒二次优化问题建立了精确的 SDP 重构。作为应用，我们为分数可调鲁棒二次优化问题建立了相应的结果。