Robust tracking error optimization problems by second-order cone programming

Recently, a robust optimization model is proposed to portfolio selection problems in a financial market in view of uncertainty of market parameters. Assuming that the uncertain parameters are not specified exactly but they are known to belong to a given set, the robust optimization problem is to find an optimal solution when the parameters take worst-case values. We consider a robust tracking error optimization problem which is one of the portfolio selection problems. It is known that the problem is reduced to a semidefinite programming problem, meanwhile we reduce it to a second-order cone programming problem which has a more simple structure than that of a semidefinite programming problem. Both the semidefinite programming and second-order cone programming are convex optimization problems, and a second-order cone programming problem usually can be solved more easily than a semidefinite programming problem. In the latter half of the paper, we present computational experiments, and we demonstrate that our model can be solved more quickly than the existing model, especially when the number of variables of a robust tracking error optimization problem is large.