ABSOLUTE VALUE EQUATIONS WITH DATA UNCERTAINTY IN THE l₁ AND l_∞ NORM BALLS

Absolute value equations (AVEs) have attracted much attention in recent studies. However, the problem data may be contaminated by noises that yield a meaningless solution, even if these coefficients are uncertain within a certain range. To address this issue, we import the idea of robust optimization and present their robust counterpart models with data uncertainty in the l₁ and l_∞ norm balls. In particular, we prove that these models are equivalent to the linear programming problems. Numerical experiments demonstrate that the true solution of these AVEs can be recovered by solving the equivalent linear programming models with open-resource packages JuMP and HiGHS in Julia language.