| Title:
|
Přehled deterministických a stochastických aproximačních metod pro minimalizaci funkcí (Czech) |
| Title:
|
A review of deterministic and stochastic approximation methods for function minimization (English) |
| Author:
|
Fabian, Václav |
| Language:
|
Czech |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
1 |
| Issue:
|
6 |
| Year:
|
1965 |
| Pages:
|
(499)-523 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| MSC:
|
62L20 |
| MSC:
|
65K10 |
| idZBL:
|
Zbl 0171.16601 |
| . |
| Date available:
|
2009-09-24T15:37:38Z |
| Last updated:
|
2012-06-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125290 |
| . |
| Reference:
|
Ablow C. M., G. Brigham (1955): An analog solution of programming problems.OR 3, 388 to 394. MR 0073323 |
| Reference:
|
Abrham J. (1958): Přibližná metoda pro nelinearní programování.Čas. pěst. mat. 83, 425-439. MR 0101503 |
| Reference:
|
Abrham J. (1961): An Approximate Method for Convex Programming.Econometrica 29, 700 to 703. MR 0138507 |
| Reference:
|
Abrham J. (1962): The Multiplex Method and its Application to Concave Programming.CZM 12, 325-345. MR 0145988 |
| Reference:
|
Ackoff R. L. (1961): Progress in Operations Research.Vol. I. John Wiley & Sons. Inc., New York - London. MR 0121239 |
| Reference:
|
Akaike H. (1959): On successive transformation of probability distribution and its application to the analysis of the optimum gradient method.Ann. Inst. Statist. Math. Tokyo 11, 1 - 16. MR 0107973 |
| Reference:
|
Altman M. (1964): Stationary points in non-linear programming.Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 12, 29-35. MR 0164810 |
| Reference:
|
Archer D. H. (1960): An optimising control for the chemical process industries.Britisch Chemical Engineering, 88 -94. |
| Reference:
|
Arnoff E. L., S. S. Sengupta (1961): Mathematical Programming.Viz sb. Ackoff (1961), 105-210. MR 0121245 |
| Reference:
|
Arrow K. J., L. Hurwicz (1951): A gradient method for approximation of saddle points and conditionned maxima.Rep. 253 RAND Corporation, June 13. |
| Reference:
|
Arrow K. J., L. Hurwicz (1956): Reduction of constrained maxima to saddle-point problems.Proc. 3rd Berkeley Symp. Math., Statist. Probability, vol. V, 1 - 20, Un. Calif. Press. MR 0084938 |
| Reference:
|
Arrow K. J., L. Hurwicz H. Uzawa (1958): Studies in Linear and Non-linear Programming.Stanford University Press, Stanford, California. MR 0108399 |
| Reference:
|
Beale E. M. L. (1955): On optimising a convex function subject to linear inequalities.JRSS B 17, 173-184. MR 0089101 |
| Reference:
|
Beale E. M. L. (1958): On an iterative method for finding a local minimum of a function of more than one variable.Statist. Tech. Research Group Techn. Report No. 25, Princeton Univ., Princeton, N. Y. |
| Reference:
|
Beale E. M. L. (1959): On quadratic programming.Naval Research Logistic Quart. 6, 227 - 243. MR 0113722 |
| Reference:
|
Bellman R. (1957): Dynamic Programming.Princeton University Press, Princeton, N. Y. MR 0090477 |
| Reference:
|
Block H. D. (1957): On stochastic approximation.ONR Report, Dept. of Mathematics. Cornell University, Ithaca, New York, 13 pp. |
| Reference:
|
Blum J. R. (1954a): Approximation methods which converge with probability one.AMS 25, 382 to 386. MR 0062399 |
| Reference:
|
Blum J. R. (1954b): Multidimensional stochastic approximation methods.AMS 25, 463 - 483. MR 0065092 |
| Reference:
|
Blum J. R. (1958): A note on stochastic approximation.Proc. Am. Math. Soc., 9, 404-407. MR 0098426 |
| Reference:
|
Both A. D. (1949): An application of the method of steepest descent to the solution of systems of non-linear simultaneous equations.Quar. J. Mech. Appl. Math. 2, 460 -468. MR 0035119 |
| Reference:
|
Box G. E. P., K. B. Wilson (1951): On the experimental attainment of optimum conditions.JRSS B 13, 1-45. MR 0046009 |
| Reference:
|
Box G. E. P. (1954): The exploration and exploitation of response surfaces: some general considerations and examples.Biometrics 10, 16-60. |
| Reference:
|
Box G. E. P., P. V. Youle (1955): The exploration and exploitation of response surfaces: an example of the link between the fitted surface and the basic mechanism of the system.Biometrics 11, 287-323. |
| Reference:
|
Box G. E. P. (1957): Evolutionary operation: a method for increasing industrial productivity.Applied Statistics 6, 81 - 101. |
| Reference:
|
Box G. E. P., J. S. Hunter (1959): Condensed calculations for evolutionary operation programs.Technometrics, 77-95. MR 0107950 |
| Reference:
|
Brooks S. H. (1959): A comparison of maximum seeking methods.J. Oper. Research Soc. 7, 430-457. |
| Reference:
|
Brownlee K. A. J. L. Hodges, Jr., M. Rosenblatt (1963): The Up-and-Down method with small samples.JASA 48, 262-277. MR 0055644 |
| Reference:
|
Burkholder D. L. (1956): On a certain class of stochastic approximation procedures.AMS 27, 1044-1059. MR 0085653 |
| Reference:
|
Carroll Ch. W. (1961): The created response surface technique for non-linear restrained systems.OR 9, 169-185. MR 0129020 |
| Reference:
|
Cauchy A. (1847): Méthode générale pour la résolution des systèms d'equations simultanées.Compte Rendu, Ac. Sci. Paris, 25, 536-538. |
| Reference:
|
Cheney E. W., A. A. Goldstein (1959): Newton's method of convex programming and Tchebycheff approximation.Numerische Math. 1, 253 - 268. MR 0109430 |
| Reference:
|
Chung K. L. (1954): On a stochastic approximation method.AMS 25, 463 - 483. MR 0064365 |
| Reference:
|
Crockett J. B., H. Chernoff (1955): Gradient methods of maximization.Pacif. J. Math. 5, 33-50. MR 0075676 |
| Reference:
|
Curry H. B. (1944): The method of steepest descent for non-linear minimization problems.Quarterly Appl. Math. 2, 258-261. MR 0010667 |
| Reference:
|
DeLand E. C. (1959): Continuous programming methods on an analog computer.Rand Corpor. Paper No. P-1815, Sept. |
| Reference:
|
Derman C. (1956): An application of Chung's lemma to the Kiefer-Wolfowitz stochastic approximation procedure.AMS 27, 532-536. MR 0078595 |
| Reference:
|
Derman C. (1956): Stochastic approximation.AMS 27, 879-886. MR 0088133 |
| Reference:
|
Derman C. (1957): Non-parametric Up-and-Down experimentations.AMS 28, 795 - 798. MR 0090956 |
| Reference:
|
Derman C., J. Sacks (1959): On Dvoretzky's stochastic approximation theorem.AMS 30, 601-606. MR 0107893 |
| Reference:
|
Dixon W. J., A. M. Mood (1948): A method for obtaining and analyzing sensitivity data.JASA 43, 109-126. |
| Reference:
|
Driml M., O Hanš (1960): On experience theory problems.PRTR2, 93 - 111. MR 0142189 |
| Reference:
|
Driml M., O. Hanš (1960): Continuous stochastic approximation.PRTR2, 113-122. MR 0130702 |
| Reference:
|
Driml M., J. Nedoma (1960): Stochastic approximation for continuous random processes.PRTR2, 145-158. MR 0126877 |
| Reference:
|
Dupač V. (1957): O Kiefer-Wolfowitzově aproximační metodě.Čas. pěst. mat. 82, 47 - 75. MR 0089556 |
| Reference:
|
Dupač V. (1958): Notes on stochastic approximation methods.CZM 8 (83), 139-149. MR 0096301 |
| Reference:
|
Dupač V. (1965a): A dynamic stochastic approximation method.V tisku v AMS 36. MR 0193724 |
| Reference:
|
Dupač V. (1965b): A dynamical stochastic approximation method.Referát na 4. pražské konferenci o teorii informace, statistických rozhodovacích funkcích a náhodných procesech. |
| Reference:
|
Dvoretzky A. (1956): On stochastic approximation.Proc. Third. Berkeley Symp. Math. Statistics and Probability, Vol. I, 39-55. University of California Press. MR 0084911 |
| Reference:
|
Fabian V. (1960): Stochastic approximation methods.CZM 10 (85), 123-159. MR 0113253 |
| Reference:
|
Fabian V. (1961): Stochastická aproximační metoda pro hledání optimálních podmínek v experimentální práci a v samoadaptivních systémech.Aplikace matematiky, 6, 162-183. MR 0131896 |
| Reference:
|
Fabian V. (1962): Blokové logické schema automatického optimalizátoru.Aplikace matematiky 7, 426-440. |
| Reference:
|
Fabian V. (1964): A new one-dimensional stochastic approximation method for finding a local minimum of a function.PRTR3, 85-105. MR 0169317 |
| Reference:
|
Fabian V. (1965): Stochastic approximation of constrained minima.Referát na 4. pražské konferenci o teorii informace, statistických rozhodovacích funkcích a náhodných procesech. |
| Reference:
|
Fabius J. (1959): Stochastic approximation.Statistics Neerlandica 13, 445-452. MR 0132597 |
| Reference:
|
Фаддеев Д. К. B. H. Фаддеевa (1963): Вычислительные методы линейной алгебры.Москва. |
| Reference:
|
Farkas J. (1902): Über die Theorie der einfachen Ungleichungen.Zeit. Reine Angew. Math. 124, 1-24. |
| Reference:
|
Farrell R. H. (1962): Bounded length confidence intervals for the zero of a regression funkction.AMS 33, 237-247. MR 0137231 |
| Reference:
|
Фельдбаум А. А. (1958): Автоматический оптимизатор.Автоматика и телемeхaника 14, 731-743. |
| Reference:
|
Fiacco A. V., G. P. McCormick (1964a): The sequential unconstrained minimization technique for nonlinear programming, a primal-dual method.Management Science 10, 360 - 366. MR 1058438 |
| Reference:
|
Fiacco A. V., G. P. McCormick (1964b): Computational algorithm for the sequential unconstrained minimization technique for nonlinear programming.Management Science 10, 601-617. |
| Reference:
|
Finkel R. W. (1959): The method of resultant descents for the minimization of an arbitrary function.Space Technology Lab. Tech. Report, Los Angeles. |
| Reference:
|
Fletcher R., M. J. D. Powell (1963/4): A rapidly convergent descent method for minimization.Comp. J. 6, 163 - 168. MR 0152116 |
| Reference:
|
Forsythe A. I., G. E. Forsythe (1952): Punched-cards experiments with accelerated gradient method for linear equations.NBS Report 1643, National Bureau of Standards, Los Angeles. |
| Reference:
|
Forsythe G. E., T. S. Motzkin (1951): Assymptotic properties of the optimum gradient method.Bull. Amer. Math. Soc. 57, 73. |
| Reference:
|
Forsythe G. E. (1953): Solving linear algebraic expressions can be interesting.Bull. Amer. Math. Soc. 59, 299-329. MR 0056372 |
| Reference:
|
Forsythe G. E., W. R. Wasow (1959): Finite-difference methods for partial difference equations.New York, Wiley & Sons. |
| Reference:
|
Фридман B. M. (1962): О сходимости методов типа найскорейшего спуска.Усп. мат. наук 17, 201-204. MR 0140180 |
| Reference:
|
Friedman M., L. J. Savage (1947): Planning experiments seeking maxima.Select. Techn. of Statist. Analysis. McGraw-Hill, New York. |
| Reference:
|
Friedman S.. (1963): On stochastic approximations.AMS 34, 343 - 346. MR 0144379 |
| Reference:
|
Frish R. (1957): The multiplex method for linear programming.Sankhya 18, 329-362. MR 0093430 |
| Reference:
|
Frish R. (1958): The multiplex method for linear programming.Memorandum fra Socialekonomisk Institut, Universitetet Oslo 12. |
| Reference:
|
Gardner L. A., Jr. (1963): Stochastic approximation and its application to problems of prediction and control synthesis.Internat. Symp. Nonlinear Differential Equations and Nonlinear Mech., Colorado Springs, New York -London, Acad. Press, 241 - 258. MR 0148200 |
| Reference:
|
Gardner L. A., Jr. (1964): Adaptive predictors.PRTR3. MR 0166896 |
| Reference:
|
Germansky B. (1934): Notiz über die Lösung von Extemaufgaben mittels Iteration.Z. Ang. Math. Mech. 14, 187-187. |
| Reference:
|
Гладышев Е. Г.: O стохастической аппроксимации.Теория вероятностей и прим. 10, 297-300. Zbl 1170.81475 |
| Reference:
|
Glass H., L. Cooper (1965): Sequential search: a method for solving constrained optimization problems.JACM 12, 71-82. |
| Reference:
|
Goldstein A. A. (1962): Cauchy's method of minimization.Numer. Math. 4, 146-150. MR 0141222 |
| Reference:
|
Goldstein A. A., Ward Cheney (1958): A finite algorithm for the solutions of consistent linear equations and inequalities and for the Tchebycheff approximation of inconsistent linear equations.Pacific J. Math. 8, 415-427. MR 0101505 |
| Reference:
|
Griffith R. E., R. A. Stewart (1961): A nonlinear programming technique for the optimization of continuous processing systems.Management Science 7, 379-392. MR 0134472 |
| Reference:
|
Guttman L., R. Guttman (1959): An illustration of the use of stochastic approximation methods.Biometrics 15, 551 - 559. |
| Reference:
|
Hanš O., A. Špaček (1960): Random fixed point approximation by differentiable trajectories.PRTR2, 203-213. MR 0124084 |
| Reference:
|
Hartley H. O., R. R. Hocking (1963): Convex programming by tangential approximation.Management Science 9, 600-612. MR 0154748 |
| Reference:
|
Hestens M. R. (1951): Iterative methods for solving linear equations.NAML Report 52-9, Nat. Bureau of Standards, Los Angeles, 19 pp. |
| Reference:
|
Ho Yu Chi (1962): On the stochastic approximation method and optimal filtering theory.Journal of math. analysis and applications 6, 152-154. MR 0144440 |
| Reference:
|
Hodges J. L., Jr., E. L. Lehmann (1956): Two approximation to the Robbins Monro process.Proc. 3rd Berkeley Symp. on Math. Statistics and Prob., vol. 1, 95-104. MR 0084915 |
| Reference:
|
Hooke R., T. A. Jeeves (1961): Direct search solution of numerical and statistical problems.JACM 8, 212- |
| Reference:
|
Hotelling H. (1941): Experimental determination of the maximum of a function.AMS 12, 20-46. MR 0003521 |
| Reference:
|
Householder A. S., F. L. Bauer (1960): Certain iterative methods for solving linear systems.Numerische Mathematik 2, 55-59. MR 0116464 |
| Reference:
|
Иванов B. B. (1962): Oб алгоритмах быстрого спуска.ДAH CCCP 143, 775-778. MR 0148218 |
| Reference:
|
John F. (1964): Extremum problems with inequalities as subsidiary conditions.„Studies and Essays", Courant anniversary volume, pp. 187-204. MR 0030135 |
| Reference:
|
Kantorovič L. V. (1945): On an effective method of solving extremal problems for quadratic functional.C. R. de l'Ac. Sci. de l'URSS XLVIII, no. 7, 455-459. MR 0016528 |
| Reference:
|
Канторович Л. B. (1945): 0б oднom методе решения экстремальных задач для квадратных функциохалов.ДАН CCCP 48, 483-487. |
| Reference:
|
Канторович Л. B. (1947): О методе найскорейшего спуска.ДAH CCCP 56, 233-236 MR 0023126 |
| Reference:
|
Канторович Л. B. (1948): Функциональный анализ и прокладная математика.Усп. мат. наук 3, 89-185. MR 0027947 |
| Reference:
|
Kelley J. E. (1960): The cutting-plane method for solving convex programs.JSIAM 8, 703-712. MR 0118538 |
| Reference:
|
Kerner M. (1933): Die Differentiale in der allegemeinen Analysis.Ann. of Math. 34, 546- 572. MR 1503123 |
| Reference:
|
Kerstukos A., R. I. van Nice (1958): Optimizing process operations.Automation 5. |
| Reference:
|
Kesten H. (1958): Accelerated stochastic approximation.AMS 29, 41-59. MR 0093851 |
| Reference:
|
Kiefer J., J. Wolfowitz (1952): Stochastic estimation of the maximum of a regression function.AMS 23, 462-466. MR 0050243 |
| Reference:
|
Kiefer J. (1953): Sequential minimax search for a maximum.Proc. Amer. Math. Soc. 4, 502-506. MR 0055639 |
| Reference:
|
Kiefer J. (1957): Optimum sequential search and approximation methods under minimum regularity assumptions.JSIAM 5, 105-136. MR 0092326 |
| Reference:
|
Killianpur G. (1954): A note on the Robbins-Monro stochastic approximation method.AMS 25. MR 0062400 |
| Reference:
|
Kitagawa T. (1959): Successive processes of statistical controls (2).Met. Coll. Sci. Univ. Kyoto, Ser. A, Math. 13, 1-16. MR 0105184 |
| Reference:
|
Kizner W. (1964): A numerical method for finding solutions of nonlinear equations.JSIAM 12, 424-428. MR 0168115 |
| Reference:
|
Klingman W. R., D. M. Himmelblau (1964): Nonlinear programming with the aid of a multiplegradient summation technique.JACM 11, 400-415. MR 0175635 |
| Reference:
|
Kose T. (1956): Solutions of saddle value problems by differential equations.Econometrica 24, 59-70. MR 0077854 |
| Reference:
|
Красулина Т. П. (1962): 3амечания о некотопых процесах стохастической апроксимации.Теория вероят к прим. 7, 113-118. |
| Reference:
|
Krolak P., L. Cooper (1963): An extension of Fibonaccian search to several variables.CACM 6, 639-641. MR 0154749 |
| Reference:
|
Kuhn H. W., A. W. Tucker (1950): Nonlinear programming.Proc. 2nd Berkeley Symp. on Mathem. Statist. and Probability, Univ. of Calif. Pres., 481-492. MR 0047303 |
| Reference:
|
Lanczos C. (1952): Solution of systems of linear equations by minimized iterations.J. Res. Nat. Bureau of Standards 49, 33-53. MR 0051583 |
| Reference:
|
Levenberg K. (1944): A method for the solution of certain non-linear problems in least squares.Qu. Appl. Math. 2, 164-168. MR 0010666 |
| Reference:
|
Leżański T. (1963): Über das Minimumproblem für Funktionale in Banachschen Räumen.Math. Annalen 152, 271-274. MR 0158253 |
| Reference:
|
Maňas M. (1965): Nelineární programování.Ek. mat. obzor 1, 3-34. |
| Reference:
|
Mangasarian O. I. (1962): Duality in nonlinear programming.Qu. Appl. Math. 20, 300-302. MR 0141530 |
| Reference:
|
Mangasarian O. I. (1963): Equivalence in nonlinear programming.Naval. Res. Logist. Quart. 10, 299-306. MR 0164813 |
| Reference:
|
Manne A. S. (1953): Concave programming for gasoline blends.Rand. Corp. Paper. No. P-383. |
| Reference:
|
Marquardt D. W. (1963): An algorithm for least-squares estimation of nonlinear parameters.JSIAM 11, 431-441. MR 0153071 |
| Reference:
|
Mises R. von, H. Pollaczek-Geiringer (1929): Praktische Verfahren der Gleichungsauflösung.Z. Angew. Math. Mech. 9, 58-77. |
| Reference:
|
Nashed M. Z. (1964): The convergence of the method of steepest descent for nonlinear equations with variational or quasi-variational operators.J. Math. Mech. 13, 765-794. MR 0166638 |
| Reference:
|
Nashed M. Z. (1965): On general iterative methods of the solutions of a class of nonlinear operator equations.Math. of Computation 19, 14-24. MR 0179906 |
| Reference:
|
Nelder J. A., R. Mead (1965): A simplex method for function minimization.Comp. J. 7, 308-313. |
| Reference:
|
Newman D. J. (1960): Locating the maximum on a unimodal surface.Presented at the 18th National Meeting of Operations Res. Soc., October 1960, neuveřejněno, viz Spang (1962). |
| Reference:
|
Newman D. J. (1965): Location of the maximum on unimodal surfaces.JACM 12, 395-398. MR 0182129 |
| Reference:
|
Pietrzykowski T. (1961): On an iteration method for maximizing a concave function on a convex set.Práce ZAM, A 13. MR 0134346 |
| Reference:
|
Pietrzykowski T. (1962): On a method of approximative finding conditional maximums.Algorytmy 1, 9-15. MR 0186777 |
| Reference:
|
Powell M. J. D. (1964): An efficient method for finding the mininum of a function of several variables without calculating the derivatives.Computer Journal 7, 155-162. MR 0187376 |
| Reference:
|
Powell M. J. D. (1965): A method for minimizing a sum of squares of non-linear functions without calculating derivatives.Comp. J. 7, 303 - 307. MR 0172456 |
| Reference:
|
Reeves C. M. (1964): Algorithm 238, conjugate gradient method.CACM 7, 481. |
| Reference:
|
Remez E. (1934): Sur un procédé convergent d'approximations succesives pour determiner les polynomes d'approximation.C. R. Ac. Sci. Paris 198, 2063-2065. |
| Reference:
|
Robbins H. S. Monro (1951): A stochastic approximation method.AMS 22, 400-407. MR 0042668 |
| Reference:
|
Rosen J. B. (1960): The gradient projection method for nonlinear programming. I. Linear constrainsts.JSIAM 8, 181-217. MR 0112750 |
| Reference:
|
Rosen J. B. (1961): The gradient projection method for nonlinear programming.Part. II. Nonlinear constraints. JSIAM 9, 514-532. MR 0135991 |
| Reference:
|
Rosenbloom P. C. (1956): The method of steepest descent.Proc. of Symp. in Applied Math. vol. 6, pp. 127-176. MR 0079339 |
| Reference:
|
Rosenbrock H. H. (1960): An automatic method for finding the largest or least value of a function.Computer Journal 3, 175-184. MR 0136042 |
| Reference:
|
Saaty T. L., Bram J. (1964): Nonlinear mathematics.McGraw-Hill Book Co., New York. MR 0164812 |
| Reference:
|
Sacks J. (1958): Asymptotic distributions of stochastic approximatons.AMS 29, 373-405. MR 0098427 |
| Reference:
|
Sakrison D. J. (1962a): Design of filters for non-mean-square error performance criteria by means of a continuous adjustment procedure.Quarterly Progress Report No. 66, 189-201 and No. 67, 119-126, Research Lab. of Electronics. |
| Reference:
|
Sakrison D. J. (1962b): Application of stochastic approximation methods to system optimization.Techn. Rep. 391, July 10, Massachusetts Inst. Technology, Res. Lab. Electronics. Cambridge, Massachusetts. |
| Reference:
|
Sakrison D. J. (1963): Iterative design of optimum filters for non-mean-square error performance criteria.Trans. of the IEEE Professional Group on Information Theory 9, 161-167. |
| Reference:
|
Sakrison D. J. (1964): A continuous Kiefer-Wolfowitz procedure for random processes.AMS 35, 590-599. MR 0161445 |
| Reference:
|
Schmetterer L. (1953): Bemerkungen zum Verfahren der stochastischen Iteration.Österreichisches Ingenieur-Archiv VII, 111-117. MR 0055640 |
| Reference:
|
Schmetterer L. (1954a): Sur l'approximation stochastique.Bull. Inst. Internat. Statist. 24. 203 to 206. MR 0068790 |
| Reference:
|
Schmetterer L. (1954b): Zum Sequentialverfahren von Robbins und Monro.Monatshefte für Mathematik 58, 33-37. MR 0061328 |
| Reference:
|
Schmetterer L. (1958): Sur l'iteration stochastique.Colloques Internationaux du centre national de la recherch scientifique. 87, 55-63. MR 0107882 |
| Reference:
|
Schmetterer L. (1961): Stochastic approximation.Proc. 4th Berkeley Sympos. Math. Statist. Probab. 1, 587-609. MR 0137268 |
| Reference:
|
Schröder E. (1870): Über unendlich viele Algorithmen zur Auflösung der Gleichungen.Math. Ann. 2, 317-365. MR 1509664 |
| Reference:
|
Shah B. V., Buehler R. J., Kempthorne O. (1964): Some algorithms for minimizing a function of several variables.JSIAM 12, 74-92. MR 0165655 |
| Reference:
|
Spang H. A. III (1962): A review of minimization techniques for nonlinear functions.SIAM Review 4, 343-365. MR 0145642 |
| Reference:
|
Стаховский Р. И. (1958): Двухканальный автоматический оптимизатор.Автоматика и телемеханика, 14, 744-756. |
| Reference:
|
Stiefel E. (1952): Über einige Methoden der Relaxationsrechnung.Zeit. Angew. Math. Phys. 3, 1-33. MR 0047409 |
| Reference:
|
Stiefel E. (1955): Relaxation Methoden bester Strategie zur Lösung linearer Gleichungssysteme.Comm. Math. Helv. 29, 157-159. MR 0071119 |
| Reference:
|
Ваинбепг М. М. (1960): О сходимости метода найскорейшего спуска для нелнейных уравнений.ДАН СССР, 130, 9-12. |
| Reference:
|
Vosiková M. (1964): Asymptotické vlastnosti Kiefer-Wolfowitzovy aproximační metody.Dipl. práce, Mat.-fyz. fak. KU. |
| Reference:
|
Wells M. (1965): Algorithm 251, Function minimization [E 4].CACM 8, 169-170. |
| Reference:
|
Wetherill G. B. (1963): Sequential estimation of quantal response curves (with discussion).JRS. B 25, 1-48. |
| Reference:
|
Witzgall C. (1960): Gradient-projection methods for linear programming.Princeton Un. and IBM Corp. Rep. No. 2, |
| Reference:
|
Wolfe P. (1960): Accelerating the cutting-plane method for nonlinear programming.Rand. Corp. Paper No. P-2010. MR 0134354 |
| Reference:
|
Wolfe P. (1961): Accelerating the cutting-plane method for nonlinear programming.JSIAM 9, 481-488. MR 0134354 |
| Reference:
|
Wolfe P. (1962): Recent developments in nonlinear programming.Advance in computers, vol. 3, Acad. Press. New York, 155-187. MR 0146002 |
| Reference:
|
Wolfowitz (1952): On the stochastic approximation method of Robbins and Monro.. AMS 23, 457-561. MR 0050242 |
| Reference:
|
Wolfowitz (1956): On stochastic approximation methods.AMS 27, 1151 - 1155. MR 0086437 |
| Reference:
|
Zoutendijk G. (1959): Maximizing a function in a convex region.JRSS B 21, 338 - 355. MR 0122578 |
| Reference:
|
Zoutendijk G. (1960): Methods of feasible directions.Elsevier Publ. Co., Amsterdam-London -New York -Princeton. MR 0129119 |
| . |
