Parametric approach for correcting inconsistent linear equality system

Abstract

In this paper, an algorithm is proposed for solving a class of nonconvex fractional problems that result from the optimal correction of inconsistent linear equality systems. The main difficulty with this problem is its nonconvexity. Nevertheless, we can show that a global optimal solution to this problem can be found by solving a very simple univariate equation on a closed interval. Computing a value and a subgradient of the function in the equation consists of solving a single trust region subproblem. This function is convex and strictly increasing. As a result, we provide an alternative algorithm based on generalized Newton's direction. Numerical examples are given to illustrate the effectiveness of the proposed method.

Keywords:

• inconsistent linear system
• fractional optimization
• trust region subproblem
• generalized Newton method

AMS Subject Classification:

• F90C30
• 90C31
• 15A39

Acknowledgements

We thank the associate editor and two anonymous referees for their constructive comments.