Numerical methods for inverse problems in quadratic programming

Abstract This paper addresses a quadratic programming inverse problem that minimizes the distance between the parameters of the objective function and the right-side parameters of the constraints and their estimated values under the condition that the feasible solution is the optimal solution to the original quadratic programming problem. By employing duality theory, we first transform this problem into an optimization problem with complementarity constraints. Subsequently, we utilize the smooth Fischer-Burmeister function to handle the complementary constraints, converting the problem into a convex optimization framework. The first-order optimality conditions are then applied to reformulate the problem as a generalized equation. We also demonstrate that the generalized Jacobian elements at the solution point are non-singular, enabling the use of an inexact Newton method for solving the problem. Numerical experiments are conducted, comparing our approach with previous methods, and the results indicate that our method exhibits significantly higher computational efficiency.