Minimal Changes in the Right Hand Side Data for Correcting Linear Infeasibility Arising in Intensity-Modulated Radiation Therapy with the Generalized Newton Method
Saeed Ketabchi [a], Hossein Moosaei [b] and Ying Xiao [c]* Author for corresponding; e-mail address: sketabchi@guilan.ac.ir; hmoosaei@gmail.com; ying.xiao@jefferson.edu
Volume: Vol.41 No.5/2 (OCTOBER 2014)
Research Article
DOI:
Received: 19 September 2011, Revised: -, Accepted: 23 October 2013, Published: -
Citation: Ketabchi S., Moosaei H. and Xiao Y., Minimal Changes in the Right Hand Side Data for Correcting Linear Infeasibility Arising in Intensity-Modulated Radiation Therapy with the Generalized Newton Method, Chiang Mai Journal of Science, 2014; 41(5/2): 1439-1443.
Abstract
Intensity modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible. In this paper, we perform the minimal correction using the norm by changing just the right hand vector for inconsistent set of linear inequalities which involves no negativity of the variables. We present an efficient second order algorithm using the generalized Newton method to solve this problem. A clinical case of IMRT treatment of prostate cancer is used to illustrate the solution process.