A review of deterministic and stochastic approximation methods for function minimization
Kybernetika (1965)
- Volume: 01, Issue: 6, page (499)-523
- ISSN: 0023-5954
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topFabian, Václav. "Přehled deterministických a stochastických aproximačních metod pro minimalizaci funkcí." Kybernetika 01.6 (1965): (499)-523. <http://eudml.org/doc/28445>.
@article{Fabian1965,
author = {Fabian, Václav},
journal = {Kybernetika},
keywords = {statistics},
language = {cze},
number = {6},
pages = {(499)-523},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Přehled deterministických a stochastických aproximačních metod pro minimalizaci funkcí},
url = {http://eudml.org/doc/28445},
volume = {01},
year = {1965},
}
TY - JOUR
AU - Fabian, Václav
TI - Přehled deterministických a stochastických aproximačních metod pro minimalizaci funkcí
JO - Kybernetika
PY - 1965
PB - Institute of Information Theory and Automation AS CR
VL - 01
IS - 6
SP - (499)
EP - 523
LA - cze
KW - statistics
UR - http://eudml.org/doc/28445
ER -
References
top- Ablow C. M., G. Brigham (1955), An analog solution of programming problems, OR 3, 388 to 394. MR0073323
- Abrham J. (1958), Přibližná metoda pro nelinearní programování, Čas. pěst. mat. 83, 425-439. MR0101503
- Abrham J. (1961), An Approximate Method for Convex Programming, Econometrica 29, 700 to 703. MR0138507
- Abrham J. (1962), The Multiplex Method and its Application to Concave Programming, CZM 12, 325-345. MR0145988
- Ackoff R. L. (1961), Progress in Operations Research, Vol. I. John Wiley & Sons. Inc., New York - London. MR0121239
- 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. MR0107973
- Altman M. (1964), Stationary points in non-linear programming, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 12, 29-35. MR0164810
- Archer D. H. (1960), An optimising control for the chemical process industries, Britisch Chemical Engineering, 88 -94.
- Arnoff E. L., S. S. Sengupta (1961), Mathematical Programming, Viz sb. Ackoff (1961), 105-210. (1961) MR0121245
- Arrow K. J., L. Hurwicz (1951), A gradient method for approximation of saddle points and conditionned maxima, Rep. 253 RAND Corporation, June 13.
- 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. MR0084938
- Arrow K. J., L. Hurwicz H. Uzawa (1958), Studies in Linear and Non-linear Programming, Stanford University Press, Stanford, California. MR0108399
- Beale E. M. L. (1955), On optimising a convex function subject to linear inequalities, JRSS B 17, 173-184. MR0089101
- 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.
- Beale E. M. L. (1959), On quadratic programming, Naval Research Logistic Quart. 6, 227 - 243. MR0113722
- Bellman R. (1957), Dynamic Programming, Princeton University Press, Princeton, N. Y. MR0090477
- Block H. D. (1957), On stochastic approximation, ONR Report, Dept. of Mathematics. Cornell University, Ithaca, New York, 13 pp.
- Blum J. R. (1954a), Approximation methods which converge with probability one, AMS 25, 382 to 386. MR0062399
- Blum J. R. (1954b), Multidimensional stochastic approximation methods, AMS 25, 463 - 483. MR0065092
- Blum J. R. (1958), A note on stochastic approximation, Proc. Am. Math. Soc., 9, 404-407. MR0098426
- 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. MR0035119
- Box G. E. P., K. B. Wilson (1951), On the experimental attainment of optimum conditions, JRSS B 13, 1-45. MR0046009
- Box G. E. P. (1954), The exploration and exploitation of response surfaces: some general considerations and examples, Biometrics 10, 16-60.
- 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.
- Box G. E. P. (1957), Evolutionary operation: a method for increasing industrial productivity, Applied Statistics 6, 81 - 101.
- Box G. E. P., J. S. Hunter (1959), Condensed calculations for evolutionary operation programs, Technometrics, 77-95. MR0107950
- Brooks S. H. (1959), A comparison of maximum seeking methods, J. Oper. Research Soc. 7, 430-457.
- Brownlee K. A. J. L. Hodges, Jr., M. Rosenblatt (1963), The Up-and-Down method with small samples, JASA 48, 262-277. MR0055644
- Burkholder D. L. (1956), On a certain class of stochastic approximation procedures, AMS 27, 1044-1059. MR0085653
- Carroll Ch. W. (1961), The created response surface technique for non-linear restrained systems, OR 9, 169-185. MR0129020
- Cauchy A. (1847), Méthode générale pour la résolution des systèms d'equations simultanées, Compte Rendu, Ac. Sci. Paris, 25, 536-538.
- Cheney E. W., A. A. Goldstein (1959), Newton's method of convex programming and Tchebycheff approximation, Numerische Math. 1, 253 - 268. MR0109430
- Chung K. L. (1954), On a stochastic approximation method, AMS 25, 463 - 483. MR0064365
- Crockett J. B., H. Chernoff (1955), Gradient methods of maximization, Pacif. J. Math. 5, 33-50. MR0075676
- Curry H. B. (1944), The method of steepest descent for non-linear minimization problems, Quarterly Appl. Math. 2, 258-261. MR0010667
- DeLand E. C. (1959), Continuous programming methods on an analog computer, Rand Corpor. Paper No. P-1815, Sept.
- Derman C. (1956), An application of Chung's lemma to the Kiefer-Wolfowitz stochastic approximation procedure, AMS 27, 532-536. MR0078595
- Derman C. (1956), Stochastic approximation, AMS 27, 879-886. MR0088133
- Derman C. (1957), Non-parametric Up-and-Down experimentations, AMS 28, 795 - 798. MR0090956
- Derman C., J. Sacks (1959), On Dvoretzky's stochastic approximation theorem, AMS 30, 601-606. MR0107893
- Dixon W. J., A. M. Mood (1948), A method for obtaining and analyzing sensitivity data, JASA 43, 109-126.
- Driml M., O Hanš (1960), On experience theory problems, PRTR2, 93 - 111. MR0142189
- Driml M., O. Hanš (1960), Continuous stochastic approximation, PRTR2, 113-122. MR0130702
- Driml M., J. Nedoma (1960), Stochastic approximation for continuous random processes, PRTR2, 145-158. MR0126877
- Dupač V. (1957), O Kiefer-Wolfowitzově aproximační metodě, Čas. pěst. mat. 82, 47 - 75. MR0089556
- Dupač V. (1958), Notes on stochastic approximation methods, CZM 8 (83), 139-149. MR0096301
- Dupač V. (1965a), A dynamic stochastic approximation method, V tisku v AMS 36. MR0193724
- Dupač V. (1965b), A dynamical stochastic approximation method, Referát na 4. pražské konferenci o teorii informace, statistických rozhodovacích funkcích a náhodných procesech.
- Dvoretzky A. (1956), On stochastic approximation, Proc. Third. Berkeley Symp. Math. Statistics and Probability, Vol. I, 39-55. University of California Press. MR0084911
- Fabian V. (1960), Stochastic approximation methods, CZM 10 (85), 123-159. MR0113253
- Fabian V. (1961), Stochastická aproximační metoda pro hledání optimálních podmínek v experimentální práci a v samoadaptivních systémech, Aplikace matematiky, 6, 162-183. MR0131896
- Fabian V. (1962), Blokové logické schema automatického optimalizátoru, Aplikace matematiky 7, 426-440.
- Fabian V. (1964), A new one-dimensional stochastic approximation method for finding a local minimum of a function, PRTR3, 85-105. MR0169317
- Fabian V. (1965), Stochastic approximation of constrained minima, Referát na 4. pražské konferenci o teorii informace, statistických rozhodovacích funkcích a náhodných procesech.
- Fabius J. (1959), Stochastic approximation, Statistics Neerlandica 13, 445-452. MR0132597
- Фаддеев Д. К. B. H. Фаддеевa (1963), Вычислительные методы линейной алгебры, Москва.
- Farkas J. (1902), Über die Theorie der einfachen Ungleichungen, Zeit. Reine Angew. Math. 124, 1-24.
- Farrell R. H. (1962), Bounded length confidence intervals for the zero of a regression funkction, AMS 33, 237-247. MR0137231
- Фельдбаум А. А. (1958), Автоматический оптимизатор, Автоматика и телемeхaника 14, 731-743.
- Fiacco A. V., G. P. McCormick (1964a), The sequential unconstrained minimization technique for nonlinear programming, a primal-dual method, Management Science 10, 360 - 366. MR1058438
- Fiacco A. V., G. P. McCormick (1964b), Computational algorithm for the sequential unconstrained minimization technique for nonlinear programming, Management Science 10, 601-617.
- Finkel R. W. (1959), The method of resultant descents for the minimization of an arbitrary function, Space Technology Lab. Tech. Report, Los Angeles.
- Fletcher R., M. J. D. Powell (1963/4), A rapidly convergent descent method for minimization, Comp. J. 6, 163 - 168. MR0152116
- 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.
- Forsythe G. E., T. S. Motzkin (1951), Assymptotic properties of the optimum gradient method, Bull. Amer. Math. Soc. 57, 73.
- Forsythe G. E. (1953), Solving linear algebraic expressions can be interesting, Bull. Amer. Math. Soc. 59, 299-329. MR0056372
- Forsythe G. E., W. R. Wasow (1959), Finite-difference methods for partial difference equations, New York, Wiley & Sons.
- Фридман B. M. (1962), О сходимости методов типа найскорейшего спуска, Усп. мат. наук 17, 201-204. MR0140180
- Friedman M., L. J. Savage (1947), Planning experiments seeking maxima, Select. Techn. of Statist. Analysis. McGraw-Hill, New York.
- Friedman S.. (1963), On stochastic approximations, AMS 34, 343 - 346. MR0144379
- Frish R. (1957), The multiplex method for linear programming, Sankhya 18, 329-362. MR0093430
- Frish R. (1958), The multiplex method for linear programming, Memorandum fra Socialekonomisk Institut, Universitetet Oslo 12.
- 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. MR0148200
- Gardner L. A., Jr. (1964), Adaptive predictors, PRTR3. MR0166896
- Germansky B. (1934), Notiz über die Lösung von Extemaufgaben mittels Iteration, Z. Ang. Math. Mech. 14, 187-187.
- Гладышев Е. Г., O стохастической аппроксимации, Теория вероятностей и прим. 10, 297-300. Zbl1170.81475
- Glass H., L. Cooper (1965), Sequential search: a method for solving constrained optimization problems, JACM 12, 71-82.
- Goldstein A. A. (1962), Cauchy's method of minimization, Numer. Math. 4, 146-150. MR0141222
- 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. MR0101505
- Griffith R. E., R. A. Stewart (1961), A nonlinear programming technique for the optimization of continuous processing systems, Management Science 7, 379-392. MR0134472
- Guttman L., R. Guttman (1959), An illustration of the use of stochastic approximation methods, Biometrics 15, 551 - 559.
- Hanš O., A. Špaček (1960), Random fixed point approximation by differentiable trajectories, PRTR2, 203-213. MR0124084
- Hartley H. O., R. R. Hocking (1963), Convex programming by tangential approximation, Management Science 9, 600-612. MR0154748
- Hestens M. R. (1951), Iterative methods for solving linear equations, NAML Report 52-9, Nat. Bureau of Standards, Los Angeles, 19 pp. (19 p)
- Ho Yu Chi (1962), On the stochastic approximation method and optimal filtering theory, Journal of math. analysis and applications 6, 152-154. MR0144440
- 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. MR0084915
- Hooke R., T. A. Jeeves (1961), Direct search solution of numerical and statistical problems, JACM 8, 212-
- Hotelling H. (1941), Experimental determination of the maximum of a function, AMS 12, 20-46. MR0003521
- Householder A. S., F. L. Bauer (1960), Certain iterative methods for solving linear systems, Numerische Mathematik 2, 55-59. MR0116464
- Иванов B. B. (1962), Oб алгоритмах быстрого спуска, ДAH CCCP 143, 775-778. MR0148218
- John F. (1964), Extremum problems with inequalities as subsidiary conditions, „Studies and Essays", Courant anniversary volume, pp. 187-204. MR0030135
- 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. MR0016528
- Канторович Л. B. (1945), 0б oднom методе решения экстремальных задач для квадратных функциохалов, ДАН CCCP 48, 483-487.
- Канторович Л. B. (1947), О методе найскорейшего спуска, ДAH CCCP 56, 233-236 MR0023126
- Канторович Л. B. (1948), Функциональный анализ и прокладная математика, Усп. мат. наук 3, 89-185. MR0027947
- Kelley J. E. (1960), The cutting-plane method for solving convex programs, JSIAM 8, 703-712. MR0118538
- Kerner M. (1933), Die Differentiale in der allegemeinen Analysis, Ann. of Math. 34, 546- 572. MR1503123
- Kerstukos A., R. I. van Nice (1958), Optimizing process operations, Automation 5.
- Kesten H. (1958), Accelerated stochastic approximation, AMS 29, 41-59. MR0093851
- Kiefer J., J. Wolfowitz (1952), Stochastic estimation of the maximum of a regression function, AMS 23, 462-466. MR0050243
- Kiefer J. (1953), Sequential minimax search for a maximum, Proc. Amer. Math. Soc. 4, 502-506. MR0055639
- Kiefer J. (1957), Optimum sequential search and approximation methods under minimum regularity assumptions, JSIAM 5, 105-136. MR0092326
- Killianpur G. (1954), A note on the Robbins-Monro stochastic approximation method, AMS 25. MR0062400
- Kitagawa T. (1959), Successive processes of statistical controls (2), Met. Coll. Sci. Univ. Kyoto, Ser. A, Math. 13, 1-16. MR0105184
- Kizner W. (1964), A numerical method for finding solutions of nonlinear equations, JSIAM 12, 424-428. MR0168115
- Klingman W. R., D. M. Himmelblau (1964), Nonlinear programming with the aid of a multiplegradient summation technique, JACM 11, 400-415. MR0175635
- Kose T. (1956), Solutions of saddle value problems by differential equations, Econometrica 24, 59-70. MR0077854
- Красулина Т. П. (1962), 3амечания о некотопых процесах стохастической апроксимации, Теория вероят к прим. 7, 113-118.
- Krolak P., L. Cooper (1963), An extension of Fibonaccian search to several variables, CACM 6, 639-641. MR0154749
- Kuhn H. W., A. W. Tucker (1950), Nonlinear programming, Proc. 2nd Berkeley Symp. on Mathem. Statist. and Probability, Univ. of Calif. Pres., 481-492. MR0047303
- Lanczos C. (1952), Solution of systems of linear equations by minimized iterations, J. Res. Nat. Bureau of Standards 49, 33-53. MR0051583
- Levenberg K. (1944), A method for the solution of certain non-linear problems in least squares, Qu. Appl. Math. 2, 164-168. MR0010666
- Leżański T. (1963), Über das Minimumproblem für Funktionale in Banachschen Räumen, Math. Annalen 152, 271-274. MR0158253
- Maňas M. (1965), Nelineární programování, Ek. mat. obzor 1, 3-34.
- Mangasarian O. I. (1962), Duality in nonlinear programming, Qu. Appl. Math. 20, 300-302. MR0141530
- Mangasarian O. I. (1963), Equivalence in nonlinear programming, Naval. Res. Logist. Quart. 10, 299-306. MR0164813
- Manne A. S. (1953), Concave programming for gasoline blends, Rand. Corp. Paper. No. P-383.
- Marquardt D. W. (1963), An algorithm for least-squares estimation of nonlinear parameters, JSIAM 11, 431-441. MR0153071
- Mises R. von, H. Pollaczek-Geiringer (1929), Praktische Verfahren der Gleichungsauflösung, Z. Angew. Math. Mech. 9, 58-77.
- 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. MR0166638
- Nashed M. Z. (1965), On general iterative methods of the solutions of a class of nonlinear operator equations, Math. of Computation 19, 14-24. MR0179906
- Nelder J. A., R. Mead (1965), A simplex method for function minimization, Comp. J. 7, 308-313.
- 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). (1960)
- Newman D. J. (1965), Location of the maximum on unimodal surfaces, JACM 12, 395-398. MR0182129
- Pietrzykowski T. (1961), On an iteration method for maximizing a concave function on a convex set, Práce ZAM, A 13. MR0134346
- Pietrzykowski T. (1962), On a method of approximative finding conditional maximums, Algorytmy 1, 9-15. MR0186777
- 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. MR0187376
- 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. MR0172456
- Reeves C. M. (1964), Algorithm 238, conjugate gradient method, CACM 7, 481.
- Remez E. (1934), Sur un procédé convergent d'approximations succesives pour determiner les polynomes d'approximation, C. R. Ac. Sci. Paris 198, 2063-2065. (198,)
- Robbins H. S. Monro (1951), A stochastic approximation method, AMS 22, 400-407. MR0042668
- Rosen J. B. (1960), The gradient projection method for nonlinear programming. I. Linear constrainsts, JSIAM 8, 181-217. MR0112750
- Rosen J. B. (1961), The gradient projection method for nonlinear programming, Part. II. Nonlinear constraints. JSIAM 9, 514-532. MR0135991
- Rosenbloom P. C. (1956), The method of steepest descent, Proc. of Symp. in Applied Math. vol. 6, pp. 127-176. MR0079339
- Rosenbrock H. H. (1960), An automatic method for finding the largest or least value of a function, Computer Journal 3, 175-184. MR0136042
- Saaty T. L., Bram J. (1964), Nonlinear mathematics, McGraw-Hill Book Co., New York. MR0164812
- Sacks J. (1958), Asymptotic distributions of stochastic approximatons, AMS 29, 373-405. MR0098427
- 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.
- 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.
- 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.
- Sakrison D. J. (1964), A continuous Kiefer-Wolfowitz procedure for random processes, AMS 35, 590-599. MR0161445
- Schmetterer L. (1953), Bemerkungen zum Verfahren der stochastischen Iteration, Österreichisches Ingenieur-Archiv VII, 111-117. MR0055640
- Schmetterer L. (1954a), Sur l'approximation stochastique, Bull. Inst. Internat. Statist. 24. 203 to 206. MR0068790
- Schmetterer L. (1954b), Zum Sequentialverfahren von Robbins und Monro, Monatshefte für Mathematik 58, 33-37. MR0061328
- Schmetterer L. (1958), Sur l'iteration stochastique, Colloques Internationaux du centre national de la recherch scientifique. 87, 55-63. MR0107882
- Schmetterer L. (1961), Stochastic approximation, Proc. 4th Berkeley Sympos. Math. Statist. Probab. 1, 587-609. MR0137268
- Schröder E. (1870), Über unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Ann. 2, 317-365. MR1509664
- Shah B. V., Buehler R. J., Kempthorne O. (1964), Some algorithms for minimizing a function of several variables, JSIAM 12, 74-92. MR0165655
- Spang H. A. III (1962), A review of minimization techniques for nonlinear functions, SIAM Review 4, 343-365. MR0145642
- Стаховский Р. И. (1958), Двухканальный автоматический оптимизатор, Автоматика и телемеханика, 14, 744-756.
- Stiefel E. (1952), Über einige Methoden der Relaxationsrechnung, Zeit. Angew. Math. Phys. 3, 1-33. MR0047409
- Stiefel E. (1955), Relaxation Methoden bester Strategie zur Lösung linearer Gleichungssysteme, Comm. Math. Helv. 29, 157-159. MR0071119
- Ваинбепг М. М. (1960), О сходимости метода найскорейшего спуска для нелнейных уравнений, ДАН СССР, 130, 9-12.
- Vosiková M. (1964), Asymptotické vlastnosti Kiefer-Wolfowitzovy aproximační metody, Dipl. práce, Mat.-fyz. fak. KU.
- Wells M. (1965), Algorithm 251, Function minimization [E 4], CACM 8, 169-170.
- Wetherill G. B. (1963), Sequential estimation of quantal response curves (with discussion), JRS. B 25, 1-48.
- Witzgall C. (1960), Gradient-projection methods for linear programming, Princeton Un. and IBM Corp. Rep. No. 2,
- Wolfe P. (1960), Accelerating the cutting-plane method for nonlinear programming, Rand. Corp. Paper No. P-2010. MR0134354
- Wolfe P. (1961), Accelerating the cutting-plane method for nonlinear programming, JSIAM 9, 481-488. MR0134354
- Wolfe P. (1962), Recent developments in nonlinear programming, Advance in computers, vol. 3, Acad. Press. New York, 155-187. MR0146002
- Wolfowitz (1952), On the stochastic approximation method of Robbins and Monro, . AMS 23, 457-561. MR0050242
- Wolfowitz (1956), On stochastic approximation methods, AMS 27, 1151 - 1155. MR0086437
- Zoutendijk G. (1959), Maximizing a function in a convex region, JRSS B 21, 338 - 355. MR0122578
- Zoutendijk G. (1960), Methods of feasible directions, Elsevier Publ. Co., Amsterdam-London -New York -Princeton. MR0129119
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