Nonlinear optimization program based on a Sequential Quadratic Programming method

This paper presents a nonlinear optimization program that is based on a SQP (Sequential Quadratic Programming) method. This program has the following characteristics: (1) Increased efficiency and reliability by automatically choosing the QP (Quadratic Programming) problem solver from between the Goldfarb-Idnani method, which is efficient, and the Least Squares method, which is reliable. (Methods are evaluated through numerical analyses.) (2) Monitoring of positive definiteness of the approximated Hesse matrix. When this matrix becomes ill-conditioned, the program resets the matrix to a unit matrix and continues the optimization. In deciding whether or not the ill condition exists, the program evaluates the matrix at all five points during each iteration. As previously known, the SQP method requires effective monitoring in order to ensure global convergency. Therefore, this program is sufficient enough to solve general nonlinear programming problems due to its aforementioned improvements. [In Japanese.]