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

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Abstract
Methods for solving this problem are considered with particular reference to achieving maximum efficiency. A streamlined version of Fletcher's (1971) method for quadratic programming is considered and also a new approach based on the use of partial LDLT factorizations. Results on a wide variety of test problems indicate that the LDLT method is superior in both efficiency and error control. This method can often be expected to solve the problem in a time comparable to that required for a Choleski factorization, and always in a small multiple of this time.