Abstract
An improved version of an unconstrained optimization algorithm based upon a homogeneous function is presented. The method is numerically stable and uses the Bartels—Golub factorization instead of Householder's modification formula. Several numerical tests indicate that the proposed method is robust and very efficient.
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R.H. Bartels and G.H. Golub, “The simplex method of linear programming usingLU decomposition”,Communications of the Association for Computing Machinery 12 (1969) 266.
D.H. Jacobson and W. Oksman, “An algorithm that minimizes homogeneous functions ofN variables inN + 2 iterations and rapidly minimizes general functions”,Journal of Mathematical Analysis and Applications 38 (1972) 535.
D.H. Jacobson and L.M. Pels, “A modified homogeneous algorithm for function minimization”,Journal of Mathematical Analysis and Applications 46 (1974) 533.
M.J.D. Powell, “A view of minimization algorithm that do not require derivatives”, Report C.S.S. 9, Atomic Energy Research Establishment, Harwell, England (June 1974).
M.J.D. Powell, “A view of unconstrained optimization”, Report C.S.S. 14, Atomic Energy Research Establishment, Harwell, England (January 1975).
M.J.D. Powell, “Some global convergence properties of a variable metric algorithm for minimization without exact line searches”, Report C.S.S. 15, Atomic Energy Research Establishment, Harwell, England (April 1975).
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Kowalik, J.S., Ramakrishnan, K.G. A numerically stable optimization method based on A homogeneous function. Mathematical Programming 11, 50–66 (1976). https://doi.org/10.1007/BF01580370
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DOI: https://doi.org/10.1007/BF01580370