A penalty-type method for solving inverse optimal value problem in second-order conic programming

Abstract

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.