A MAJORIZED PENALTY APPROACH TO INVERSE LINEAR SECOND ORDER CONE PROGRAMMING PROBLEMS

This paper focuses on a type of inverse linear second order cone programming (LSOCP) problems which require us to adjust the parameters in both the objective function and the constraint set of a given LSOCP problem as little as possible so that a known feasible solution becomes optimal one. This inverse problem can be formulated as a linear second order cone complementarity constrained optimization problem and is difficult to solve due to the presence of second order cone complementarity constraint. To solve this difficult problem, we first partially penalize the inverse problem and then propose the majorization approach to the penalized problem by solving a sequence of convex optimization problems with quadratic objective function and simple second order cone constraints. Numerical results demonstrate the efficiency of our approach to inverse LSOCP problems.