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A generalized conjugate gradient algorithm for minimization. (English) Zbl 0424.65033

MSC:
65K05 Numerical mathematical programming methods
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References:
[1] Stoer J (1977) On the relation between quadratic termination and convergence properties of minimization algorithms, Part I, Theory. Numer Math 28: 343-366 · Zbl 0366.65027 · doi:10.1007/BF01389973
[2] Baptist P, Stoer J (1977) On the relation between quadratic termination and convergence properties of minimization algorithms, Part II. Numer Math 28: 367-391 · Zbl 0366.65028 · doi:10.1007/BF01404342
[3] Dixon LCW (1975) Conjugate gradient algorithms: Quadratic termination properties without line searches. J Inst Math Appl, 15: 9-18 · Zbl 0294.90076 · doi:10.1093/imamat/15.1.9
[4] Nazareth L (1977) A conjugate direction algorithm without line searches. JOTA, 3: 373-387 · Zbl 0348.65061 · doi:10.1007/BF00933447
[5] Best MJ (1975) A method to accelerate the rate of convergence of a class of optimization algorithms. Math Programming, 9: 139-160 · Zbl 0352.90053 · doi:10.1007/BF01681341
[6] Sloboda F (1979) An imperfect conjugate gradient algorithm. Report No. 58, Mathemat. Institute der Universität Würzburg: 1-13 · Zbl 0403.90061
[7] Boland WR, ER Kamgnia, JS Kowalik (1979) A conjugate gradient optimization method invariant to nonlinear scaling. JOTA 27: 221-230 · Zbl 0396.49024 · doi:10.1007/BF00933228
[8] Kowalik JS, KC Ramakrishnan (1976) A numerically stable optimization method based on a homogeneous function. Math Programming 11: 50-66 · Zbl 0351.90052 · doi:10.1007/BF01580370
[9] Jacobson DH, W Oksmann (1972) An algorithm that minimizes homogeneous functions ofN variables inN+2 iterations and rapidly minimizes general functions. J Math Anal Appl 38: 535-545 · Zbl 0234.65063 · doi:10.1016/0022-247X(72)90067-4
[10] Biggs MC (1971) Minimization algorithms making use of non-quadratic properties of the objective function. J Inst Math Appl 8: 315-327 · Zbl 0226.90045 · doi:10.1093/imamat/8.3.315
[11] v Hottenbalken B (1975) A finite algorithm to maximize certain pseudoconcave functions on polytopes. Math Programming 8: 189-206 · Zbl 0323.90042
[12] Boland WR, JS Kowalik (1979) Extended conjugate gradient methods with restarts. JOTA 28: 1-9 · Zbl 0416.49019 · doi:10.1007/BF00933597
[13] Kowalik JS, Kamgnia ER (1979) An exponential function as a model for a conjugate gradient optimization method. J Math Anal Appl 67: 476-482 · Zbl 0416.65045 · doi:10.1016/0022-247X(79)90037-4
[14] Spedicato E (1976) A variable-metric method for function minimization derived from invariancy to nonlinear scaling. JOTA, 20: 315-329 · Zbl 0316.90066 · doi:10.1007/BF00933626
[15] Spedicato E (1978) A note on the determination of the scaling parameters in a class of Quasi-Newton methods for unconstrained minimization. J Inst Math Appl 21: 285-291 · Zbl 0384.65031 · doi:10.1093/imamat/21.3.285
[16] Hestenes MR, E Stiefel (1952) The method of conjugate gradients for solving linear systems. J Res Nat Bur Standards Sect B 49: 409-436 · Zbl 0048.09901
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