This paper aims to consider a type of inverse optimal value problem in second-order conic programming, in which the parameter in its objective function needs to be adjusted under a given class that makes the corresponding optimal objective value closest to a target value. This inverse problem can be reformulated as a minimization problem with some second-order cone complementarity constraints. To tackle these bilinear constraints, we apply a penalty-type method and show that the associated penalty term is exact, which avoids the hurdles of penalty-type methods in the update strategy of the penalty parameter. Numerical results show that our method is suitable to solve the given inverse optimal value problem under different metric distances between the optimal value of the forward problem and a target objective counterpart.

中文翻译：

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求解二阶圆锥规划逆最优值问题的惩罚型方法

本文旨在考虑二阶二次曲线规划中的一类逆最优值问题，其中需要在给定类别下调整其目标函数中的参数，使得相应的最优目标值最接近目标值。这个反问题可以重新表述为具有一些二阶锥体互补约束的最小化问题。为了解决这些双线性约束，我们应用了惩罚型方法并证明了相关的惩罚项是精确的，这避免了惩罚型方法在惩罚参数更新策略中的障碍。数值结果表明，我们的方法适合解决给定的逆最优值问题，在正向问题的最优值与目标目标对应物之间的不同度量距离下。