论文标题
关于二元性，替代性的定理和圆锥优化的预测
On strong duality, theorems of the alternative, and projections in conic optimization
论文作者
论文摘要
圆锥程序是在与另一个锥体的仿射预先图像相交的封闭凸锥上优化线性函数的问题。我们分析了三个约束资格，即封闭性CQ，Slater CQ和有界的CQ（也称为Clark-Duffin定理），足以达到强双重性，并表明第一个意味着第二个意味着第三个，并且还为锥形问题提供了第三个CQ的更一般形式。此外，提出了强双重性的两个后果，第一个是替代方案的定理几乎可行性（也称为弱的不可行性），第二个是对线性子空间投影的明确描述，类似于使用多面体集合的投影锥。
A conic program is the problem of optimizing a linear function over a closed convex cone intersected with an affine preimage of another cone. We analyse three constraint qualifications, namely a Closedness CQ, Slater CQ, and Boundedness CQ (also called Clark-Duffin theorem), that are sufficient for achieving strong duality and show that the first implies the second which implies the third, and also give a more general form of the third CQ for conic problems. Furthermore, two consequences of strong duality are presented, the first being a theorem of the alternative on almost feasibility (also called weak infeasibility), and the second being an explicit description of the projection of conic sets onto linear subspaces, akin to using projection cones for polyhedral sets.
