Abstract
The main objective of this study is to discuss the optimum correction of linear inequality systems and absolute value equations (AVE). In this work, a simple and efficient feasible direction method will be provided for solving two fractional nonconvex minimization problems that result from the optimal correction of a linear system. We will show that, in some special-but frequently encountered-cases, we can solve convex optimization problems instead of not-necessarily-convex fractional problems. And, by using the method of feasible directions, we solve the optimal correction problem. Some examples are provided to illustrate the efficiency and validity of the proposed method.
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Acknowledgements
The authors are extremely thankful to Professor Richard W. Cottle for his careful reading of the manuscript. The paper has benefited from his suggestions and detailed comments.
The authors are also grateful to Gianni Di Pillo and two anonymous referees for their helpful comments and suggestions which led to the improvement of the originally submitted version of this work.
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Communicated by Gianni Di Pillo.
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Ketabchi, S., Moosaei, H. Optimal Error Correction and Methods of Feasible Directions. J Optim Theory Appl 154, 209–216 (2012). https://doi.org/10.1007/s10957-012-0009-6
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DOI: https://doi.org/10.1007/s10957-012-0009-6