Absolute value equations with uncertain data

Absolute value equations (AVE) provide a useful tool for optimization as they subsume many mathematical programming problems. However, in some applications, it is difficult to determine the exact values of the problem data and there may be some certain errors. Finding a solution for AVE based on erroneous data using existing approaches might yield a meaningless solution. In this paper, robust optimization, which represents errors in the problem data, is used. We prove that a robust solution can be obtained by solving a robust counterpart problem, which is equivalent to a second order cone program. The results also show that robust solutions can significantly improve the performance of solutions, especially when the size of errors in the problem is large.