Imperfect conjugate gradient algorithms for extended quadratic functions. (English) Zbl 0524.65045


65K05 Numerical mathematical programming methods
90C20 Quadratic programming
90C25 Convex programming


Zbl 0503.65017
Full Text: DOI EuDML


[1] Babtist, P., Stoer, J.: On the relation between quadratic termination and convergence properties of minimization algorithms. Part 2. Numer. Math.28, 367-391 (1977) · Zbl 0366.65028
[2] Biggs, M.C.: Minimization algorithms making use of non-quadratic properties of the objective functions. J. Inst. Math. Appl.8, 315-327 (1971) · Zbl 0226.90045
[3] Boland, W.R., Kamgnia, E.R., Kowalik, J.S.: A conjugate gradient optimization method invariant to nonlinear scaling. JOTA27, 221-230 (1979) · Zbl 0396.49024
[4] Boland, W.R., Kowalik, J.S.: Extended conjugate gradient methods with restarts. JOTA28, 1-9 (1979) · Zbl 0416.49019
[5] Hestenes, M., Stiefel, E.: The method of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards Sect. B49, 409-436 (1952) · Zbl 0048.09901
[6] Hottenbalken, B.: A finite algorithm to maximize certain pseudoconcave functions on polytopes. Math. Programming8, 189-206 (1975) · Zbl 0323.90042
[7] Jacobson, D.H., Oksmann, W.: An algorithm that minimizes homogeneous functions ofN variables inN+2 iterations and rapidly minimizes general functions. J. Math. Anal. Appl.38, 535-545 (1972) · Zbl 0234.65063
[8] Kowalik, J.S., Ramakrishnan, K.C.: A numerically stable optimization method based on a homogeneous function. Math. Programming11, 50-66 (1976) · Zbl 0351.90052
[9] Kowalik, J.S., Kamgnia, E.R.: An exponential function as a model for a conjugate gradient optimization method. J. Math. Anal. Appl.67, 476-482 (1979) · Zbl 0416.65045
[10] Shirey, J.E.: Minimization of extended quadratic functions. Numer. Math.39, 157-161 (1982) · Zbl 0491.65038
[11] Sloboda, F.: A generalized conjugate gradient algorithm for minimization. Numer. Math.35, 223-230 (1980) · Zbl 0424.65033
[12] Sloboda, F.: An imperfect conjugate gradient algorithm. Aplikace matematiky27, 426-434 (1982) · Zbl 0503.65017
[13] Spedicato, E.: A variable-metric method for function minimization derived from invariancy to nonlinear scaling. JOTA20, 315-329 (1976) · Zbl 0316.90066
[14] Spedicato, E.: A note on the determination of the scaling parameters in a class of Quasi-Newton methods for unconstrained optimization. J. Inst. Math. Appl.21, 285-291 (1978) · Zbl 0384.65031
[15] Stoer, J.: On the relation between quadratic termination and convergence properties of minimization algorithms. Part 1. Theory. Numer. Math.28, 343-366 (1977) · Zbl 0366.65027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.