论文标题
通过半决赛计算不确定线性圆锥程序的可行性半径
Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semidefinite Programs
论文作者
论文摘要
鲁棒可行性的半径为最大可能的不确定性集提供了数值，可确保不确定的线性圆锥程序的可行性。这决定了何时可行的集合是非空的。否则，不确定程序的强大对应物将不会被视为强大的优化问题。在本文中，我们解决了一个重要的优化的关键基本问题：如何计算不确定的线性圆锥程序（包括线性程序）的不确定线性圆锥程序的可行性半径？我们首先提供可计算的下限和上限，以使在常用的球不确定性集中对一般不确定的线性圆锥程序的鲁棒可行性半径。然后，我们提供重要类的线性圆锥程序，其中通过找到相关半芬矿线性程序（SDP）的最佳值来计算边界，其中包括不确定的SDP，不确定的二阶锥形程序和不确定的支持向量机器问题。在不确定的线性程序的情况下，确切的公式使我们能够通过找到相关的二阶程序的最佳值来计算半径。
The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees robust feasibility of an uncertain linear conic program. This determines when the robust feasible set is non-empty. Otherwise the robust counterpart of an uncertain program is not well-defined as a robust optimization problem. In this paper, we address a key fundamental question of robust optimization: How to compute the radius of robust feasibility of uncertain linear conic programs, including linear programs? We first provide computable lower and upper bounds for the radius of robust feasibility for general uncertain linear conic programs under the commonly used ball uncertainty set. We then provide important classes of linear conic programs where the bounds are calculated by finding the optimal values of related semidefinite linear programs (SDPs), among them uncertain SDPs, uncertain second-order cone programs and uncertain support vector machine problems. In the case of an uncertain linear program, the exact formula allows us to calculate the radius by finding the optimal value of an associated second-order cone program.
