Abstract: This paper is devoted to the study of the inverse quadratic programming. The problem can be formulated as a cone constrained optimization problem with a complementary constrain. Based on the theory of duality, we reformulate this problem as a linear complementarity constrained nonsmooth optimization problem with fewer variables than the original one. We introduce a perturbation approach to solve the reformulated problem and demonstrate the global convergence. An inexact Newton method is constructed to solve the perturbation problem and its global convergence and local quadratic rate can be obtained. In the end, our numerical experiment results show the feasibility of this method.

Key words: inverse semi-definite quadratic programming problems, perturbation approach, the convergence, inexact Newton method