Minimization of a Quadratic Function of Many Variables Subject only to Lower and Upper Bounds

Methods for solving this problem are considered with particularreference to achieving maximum efficiency. A streamlined versionof Fletcher's (1971) method for quadratic programming is consideredand also a new approach based on the use of partial LDL^T factorizations.Results on a wide variety of test problems indicate that theLDL^T method is superior in both efficiency and error control.This method can often be expected to solve the problem in atime comparable to that required for a Choleski factorization,and always in a small multiple of this time.