《《2016 The cholesky factorization in interior point methods》.pdf

An Intemdonal Journal .,_~, ~. Available online at computers • o , . . ~ - ~ o , . - o . , mathematics with applications F_LSFv2P_,R Computers and Mathematics with Applications 50 (2005) 1157-1166 /locate/camwa The Cholesky Factorization in Interior Point M e t h o d s C. M~SZ~,ROS Computer and Automation Research Institute Hungarian Academy of Sciences,Budapest mcsaba@oplab, sztaki,hu A b s t r a c t - - T h e paper concerns the Cholesky factorization of symmetric positive definite matrices arising in interior point methods. Our investigation is based on a property of the Cholesky fac- torization which interprets small diagonal values during factorization as degeneracy in the scaled optimization problem. A practical, scaling independent technique, based on the above property, is developed for the modified Cholesky factorization of interior point methods. This technique in- creases the robustness of Cholesky factorizations performed during interior point iterations when the optimization problem is degenerate. Our investigations show also the limitations of interior point methods with the recent implementation technology and floa