In this paper, we study the optimum correction of the absolute value equations through making minimal changes in the coefficient matrix and the right hand side vector and using spectral norm. This problem can be formulated as a non-differentiable, non-convex and unconstrained fractional quadratic programming problem. The regularized least squares is applied for stabilizing the solution of the fractional problem. The regularized problem is reduced to a unimodal single variable minimization problem and to solve it a bisection algorithm is proposed. The main difficulty of the algorithm is a complicated constraint optimization problem, for which two novel methods are suggested. We also present optimality conditions and bounds for the norm of the optimal solutions. Numerical experiments are given to demonstrate the effectiveness of suggested methods.

在本文中，我们通过对系数矩阵和右侧向量进行最小的更改并使用频谱范数来研究绝对值方程的最佳校正。这个问题可以表述为不可微，非凸且不受约束的分数二次规划问题。正则化最小二乘用于稳定分数问题的解。将正则化问题简化为单峰单变量最小化问题，并针对此问题提出了一种二等分算法。该算法的主要困难是复杂的约束优化问题，为此提出了两种新颖的方法。我们还提出了最优条件和最优解范数的界。数值实验证明了所提方法的有效性。