Tikhonov regularization for infeasible absolute value equations

Abstract

We investigate the optimum correction of an absolute value equation by minimally changing the coefficient matrix and right-hand side vector using Tikhonov regularization. Solving this problem is equivalent to minimizing the sum of fractional quadratic and quadratic functions. The primary difficulty with this problem is its nonconvexity. Nonetheless, we show that a global optimal solution to this problem can be found by solving an equation on a closed interval using the subgradient method. Some examples are provided to illustrate the efficiency and validity of the proposed method.

Keywords:

• Absolute value equation
• fractional programming
• optimal correction
• subgradients
• Tikhonov regularization

AMS Subject Classifications:

• 90C26
• 90C22
• 90C32
• 15A39

Notes

No potential conflict of interest was reported by the authors.