using the linear conjugate-gradient method. Report (to appear). Department of Operations Research, Stanford University, Califorma.

Гилл, Мюррей. Пмкен и Paftr

Gill P. е., Murray W., Picken S. M. and Wright M. H. (1979). The design and structure of a Fortran program library for optimization, ACM Trans, Math. Software 5. pp. 259-283.

Гилл, Мюррей и Сондерс

Gill P. е., Murray W. and Saunders M. A. (1975). Methods for computing and modifying the LDV factors of a matrix. Mathematics of Computation 29, pp. 1051- 1077.

Гилл, Мюррей, Сондерс н Райт

Gill P. е., Murray W., Saunders M. A. and Wright M. H. (1979). Two step-length algorithms for numerical optimization, Report SOL 79-25, Department of Operations Research, Stanford University, California.

----(1980). «A projected Lagrangian method for problems with both linear

and nonlinear constraints*, presented at the SIAM 1980 Fall Meeting, Houston, Texas.

----(1981a). «A numerical investigation of ellipsoid algorithms For large-scale linear programming*, in Large-Scale Linear Programming (Volume 1) (G. B. Dantzig, M. A. Dempster and M. J. Kallio, eds.), pp. 487-509, IIASA Collaborative Proceedings Series, CP-81-51, IIASA, Laxenburg, Austria.

----(1981b). QP-based methods for large-scale nonlinesrly constrained optimization. Report SOL 81-1, Department of Operations Research, Stanford University, California. To appear in Nonlinear Programming 4, (O. L. Manga-sarian, R. R. Meyer and S. M. Robinson, eds.). Academic Press, London and New York.

Глэд

Glad S. T. (1979). Properties of updating methods for the multipliers in augmented Lagrangians, J. Opt. Th. Applies 28. pp. 136-156.

Глэд и Полак

Glad S. T- and Polak E. (1979). A multiplier method with automatic limitation of penalty growth. Math. Prog. 17, pp. 140-155.

Голуб и Перейра

Golub G. H. and Pereyra V. (1973). The differentiation of pseudo-inverses and nonlinear least-squares problems whose variables separate, SIAM J. Numer. Anal. 10. pp. 413-432.

Голуб и Райнх

Golub G. H- and ReinschC. (1971). ((Singular value decomposition and least-squares solutions*, in Handbook for Automatic Computation. Vol. П (J. H. Wilkinson and C. Reinsch, eds.), pp. 134-151, Springer-Verlag, Berlin, Heidelberg and New York.

Гольдфарб

Goldfarb D. (1969). Extension of Davidais variable metric naethod to maximization under linear inequality and equality constraints. SIAM J. Appl. Math. 17, pp. 739-764.

- (1970). A family of variable metric methods derived by variational means, Ma-

thematics of Computation 24, pp. 23-26.

- (1980). Curvilinear path step tenth algorithms for minimization which use direc-

tions of negative curvature. Math. Prog. 18, pp. 31-40.

Гольдфарб и Райд

Goldfarb D- and Refd J. K- (1977). A practicable steepest-edge simplex algorithm. Math. Prog. 12, pp. 361-371.

Гольдфельд, Квандт м Goldfeld S. M., Quandt R. E. and Trotter H. F. (1966). Maximization by quadratic

hill-climbing, Econometrica 84, pp. 541-551. Гольдштейн и Прайс

Goldstein A. and Price J. (1967). An effective algorithm for minimization, Numer. Math. 10, pp. 184-189.

Гоффен

Goffin J. L. (I9fi0). Convergence results in a class of variable metric subgradient methods. Working Faper 80-08, Faculty of Management, McGill University, Montreal, Canada. To appear in Nonlinear Programming 4 (O. L. Mangasarian, R- R. Meyer and S. M. Robinson, eds.). Academic Press, London and New York.

Гринберг

GJeenberg H. J. (1978a). «A tutorial on matricial packings, in Design and Implementation of Optimization Software (H. J. Greenberg, ed.), pp. 109-142, Sijthoff and Noordhoff, Netherlands.

- (I978b). ((Pivot selection tactics*, in Design and Implementation of Optimization

Software (H. J. Greenberg, ed.), pp. 143-174. Sijthoff and Noordhoff, Netherlands.

Гринберг и Кэлан

Greenberg Н. J. and Kalan J. E. (1975). An exact update for Harris TREAD. Math. Prog. Study 4, pp. 26-29.

Грнг)штадт

Greenstadt J. L. (1967). On the relative efficiencies of gradient methods. Mathematics of C(Mnputation 21, pp, 360-367,

- (1970). Variations on variable-metric methods. Mathematics of Computation 24,

pp. 1-22.

- (1972). A quasi-Newton method with no derivatives, Mathematics of Computa-

tion 26, pp, 145-166.

Гриффит H Стюарт

Griffith R. E. and Stewart R. A, (I98I). Л nonlinear programming technique for the optimization of continuous processing systems. Management Science, 7, pp. 379-392.

Грэхем

Graham S. R, (1976). A matrix factorization and its application to unconstrained minimization. Project thesis for BSc. (Hons) in Mathematics for Business, Middlesex Polytechnic, Enfield, England.

Gay D, M, (1979a), On robust and generalized linear regression problems. Report 200, Mathematics Research Center, University of Wisconsin, Madison, Wisconsin.

- (1979b), Computing optimal locally constrained steps, Report 2013, Mathematics

Research Center, University of Wisconsin, Madison, Wisconsin.

Гэй и Шнабель

Gay D. M, and Schnabel R, B. (1978), eSolving systems of nonlinear equations by Broydens method with projected updates*, in Nonlinear Programming 3 (O. L. Managasarian, R, R, Meyer and S. M. Robinson, eds.), pp. 245-281, Academic Press. London and New York.

Дальквист и Бьёрк

Dahlquist G. and Bjorck A. (1974). Numerical Methods, Prentice-Hall Inc.. Engle-wood Cliffs, New Jersey.

Данциг

Dantzig G, B. (1963). Linear Programmin!* and Extensions, Prmceton University Press, Princeton New Jersey. (Имеется перевод; Дж. Данииг. Линейное программирование, его обобщения и применения.- М.: Прогресс. 1966.)

Данциг, Орден и Вулф

Dantzig G. В., Orden А. and WoHe P. (1955). Generalized simplex method for minimizing a linear form under linear inequality restraints, Pacific J. Math. 5, pp. 183-195.

Данциг, Демпстер и Каллио

Dantzig G. В., Dempster М. A. Н. aiidKallioM. J. (eds.) (1981). Large-Scale Linear Programming (Volume i), IfASA ColJabcretive Proceedings Scries, CP-81-5], llASA, Laxenburg, Austria.

Duf?l.s.andReid J. K. (1978). An implementation of Tarjans algorithm for the block triangularization of a matrix, ACM Trans. Math. Software 4, pp. 137- 147.

DnR.jyieSsSi and Zeiier C. (1967). Geometric Programming-Theory and Applications. John Wiley and Sens, New York and Toronto.

Деккер

Dekker T. J. (1969). «FindHig a zero by means of successive linear interpolation)!, in Constructive Aspects of the Fundamental Theorem of Algebra (B. Dejon and P. Henrici, eds.), pp. 37-48, Wiley Interscience, London,

Дембо

Dembo R. S. (1978). Current state of the ait of algorithms and computer software for geometric programming, J.Opt. Th. Applies. 26, pp. 149-184.

Дембо, Айзенштат и Штайхауг

Dembo R.S., Eisenstat S. С. and Steihaug T. (1980). Inexact Newton methods. Working Paper 47. School of Organization and Management, Yale University.

Дембо H Штайхауг

Dembo R- S. and Steihaug T. (1980). Truncated-Newton algorithms for large-scale unconstrained optimization. Working Paper # 48, School of Organization and Management, Yale University.

Деннис

Dennis J. E., Jr. (1973). «Some computational techniques for the nonlinear least-squares problems, in Numerical Solution of Systems of Nonlinear Algebraic Equations (G. D. Byrne and C. A. Hall, eds.), pp. 167-183, Academic Press, London and New York,

- (1977). aNonlinear Least Squares*, in The State of the Art In Numerical Analysis (D. Jacobs, ed.), pp. 269-312, Academic Press, London and New York.

Денннс и Море

Dennis J. е., Jr. and More J. J. (1974). A characterization of sucerlinear convergence and its application to quasi-Newton methods. Mathematics of Computation 28, pp. 549-560.

--(]977). Quasi-Newton methods, motivation and theory. SlAM Review 19,

pp. 46-89.

Деннис, Гэн н Уелш

Dennis J. е., Jr., Gay D. M. and Welsch R. E. (1977). An adaptive nonlinear least-squares algorithm, Report TR 77-321. Department of Computer Sciences, Cornell University.

Деннис и Шнлбель

Dennis J. е., Jr. and Schnabel R. e. (1979). Least change secant updates for quasi-

Newlon methods, SlAM Review 2), pp. 443-469. (1980). A new derivation of symmetric positive definite secant updates. Report

CU-CS-185-80, Department of Mathematical Sciences, Rice University.

Джанг

Djang A. (1980). Algorithmic Equivalence in Quadratic Programming. Ph. D. Thesis. Stanford University, California.

Джейн, Лэсдон и Сондерс

Jain А.. Lasdon L. S. and Saunders M. A. (1976). «An in-core nonlinear mathematical programming system for large nonlinear progranjs», presented at ORSA/TIiWS Joint National Meeting, Miami. Florida.

Джонсон

Johnson E. L. (1978). cSome considerations in using branch-and-bound codes*, in Design and Implementation of Optimization Software (H.J. Greenberg, ed.i, pp. 241-248. Sijthcff and Noordhoff, Netherlands.

Джонсон H Пауэлл

Johnson E. L. and Powell S. (1978). «lnteger programming codes*, in Design and Implementation of Optimization Software (H. J. Greenberg, ed.), pp. 225- 240, Sijthoff and Noordhoff, Netherlands.

Диксон

Dixon L. C. W. (1972a). Quasi-Newton algorithms generate identical points. Math. Prog. 2. pp. 383-387.

- (1972b). Quasi-Newton algorithms generate identical points. 11. The proof of

four new theorems. Math. Prog. 3, pp. 345-358.

- (1975). Conjugate-gradient algorithms: quadratic termination without linear

searches, J. Inst. Maths. Applies. 15, pp. 9-18.

Доигарра, Банч. Молер, С:тюарт

Dongarra J. J., Bunch J. R., Moler C. B. and Stewart G. W. (1979). LINPACK Users Guide, SlAM Publications, Philadelphia.

Дэвидон

Davidon W. C. (1959). Variable metric methods for minimization, A. E. C. Res. and Develop. Report ANL-5990, Aigonne National Laboratory, Argwne. Illinois.

- (1975). Optimally conditioned optimization algorithms without line searches.

Math. Prog. 9, pp. 1-30.

- (1979). Conic approximations and coilinear scalings for optimizers, SlAM J. Nu-

mer. Anal. 17, pp. 268-281.

Дэвис и Рабинович

Davis P. J. and Rabinowitz P. (1967). Numerical Integration, Blaisdell, London. Дэниел. Грэг, Каушан и Стюарт

Daniel J. W.. Grigg W. В., Kaufman L. C. and Stewart G. W. (1976). Reorthogo-nalization and stable algorithms for updating the Gram-Schmidt QR factorization. Mathematics of Computation 30. pp. 772-795.

Дюмонте и Внньес

Dumontet J. and Vignes J. (1977). Determination du pas optimal dans le calcul des derivees sur ordineur. Revue franjaise dautomatique, dinformation el de recherche operationelle. Analyse numerique (RAlRO) II, pp. 13-25.

Зангвилл

Zangwill W. I. (1965). Nonlinear programming by sequential unconstrained maximization. Working Paper 131, Center for Research in Management Science, University of California, Ba-keley.

- (1967a). Nonlinear programming via penalty functions. Management Science 13,

pp. 344 -358.

- (1967b). Algorithm for the Chebyshey problem. Management Science 14, pp. 58-

Зойтендейк

Zountendjik G. (1970). «Nonlinear programming, computational methods*, in Inte-

ger and Nonlinear Programming (J. Abadie, ed.), pp. 37-86, North-Holland, Amsterdam.

Зуховицкий СИ., Поляк P. A. и Примак М. Е. (1963). Алгоритм для решения задач ВЫПУКЛОГО чебышевского приближения.- Докл. АН СССР, 1963, т. 135. №5, с. 991-994.

Канторович Л. В. и Акилов Г. П. (1959). Функциональный анализ в нормированных пространствах.-М.: Физматгиз, 1959.

Каралаыбус

Charalambous С. (1978). А lower bound for the controlling parameter of the exact penalty function. Math. Prog. 15. pp. 278-290.

Караламбус и Конн

Charalambous С. and Conn A. R. (1978). An efficient method to solve the minlmax problem directly, SIAM J. Numer. Anal. 15. pp. 162-187.

Кауфман и Перейра

Kaufman L, С. and Pereyra V. (1978). A method for separable nonlinear least-squarea problems with separable nonlinear equality constraints, SIAM J. Numer, Anal. 15, pp. 12-20.

Kaxaii

Kahan W, (1973), The implementation of algorithms: Part 1, Technical Report 20, Department of Computer Science, University of California, Berkeley,

Келли

Kelley j. E. (1960). The cutting plane method for soiving convex programs, j. Soc. indust, Appl, Math. 8, pp. 703-712.

Кертис. Пйуэлл и Райд

Curtis А, R. Powell М. J. D. and Reid J. K. (1974). On the estimation of sparse Jacobian matrices, J. Inst, Maths. Applies. 13. pp, 117-119.

KepTHC и Райд

Curtis A. R.andReidJ. K. (1972). On the automatic scaling ol matrices for Gaussian elimination, J. Inst. Maths. Applies. Ю, pp. 118-124.

--(1974). The choice of step lengths when using differences to approximate Jacobian matrices, j. fnst. Maths, Applies. 13, pp. 121-126.

Кляйн. Молер. Стюарт и Унлкипсон

Cline А. К-. Moler С. В., Stewart G. W. and Wilkinson j. Н. (1979), An estimate for the condition number of a matrix, SIAM j. Numer. Anal. 16, pp. 368-375.

Khvt

KniJth D- E. (1979). TEX and METAFONT. New Directions in Typesetting, Ameri-caji Mathematical Society and Digital Press, Bedford, Massachusetts.

KoKc

Cox M. G. (f977). «A survey of numerical methods for data and function approxima-tiorw, in The State of the Art in Numerical Analysis (D. Jacobs, ed.), pp. 627- 668, Academic Press, London and New York-

Колвилл

Colville A. R. (1958). A comparative study on nonlinear programming codes. Report No. 320-2949, IBM New York Scientific Center.

Колеман

Coleman T. F. (1979). A Superlinear Penalty Function Method to Solve the Nonlinear Programming Problem, Ph. D. Thesis, University of Waterloo, Ontario, Canada.

Колеман и Конн

Coleman Т. F. and Conn A- R. (1980a). Second-order conditions for an exact penalty luncticn. Math. Prog. 19. pp. 178-185.

--(I980b).-Nonliix£r programming via an exact penally function method: asymptotic analysis. Report CS-80-30, Department of Computer Science, University of Waterloo, Ontario, Canada.

--(1980c). Nonlinear programming via an exact penalty function method: global

analysis, Report CS-80-31, Department of Computer Science, University of Waterloo, Olitario, Canada.

Колеман н Море

Coleman Т. F. and More J. J, (1980). «Coloring large sparse Jacobians and Hessians;), presented at the SIAM 1980 Fall Meeting, Houston, November 1980.

Конкус, Голуб и ОЛири

Concus P., Golub G. H. and OLeary D. P. (1976). «A generalized conjugate-gradient method for the numerical solution of elliptic partial differential equations», in Sparse Matrix Computations (J. R. Bunch and D. J. Rose, eds.), pp. 309-332, .Academic Press, London and New York-

KoHH

Сшп A. R. (1973). Constrained optimization using a non-different iable penalty function, SIAM J. Numer. Anal. 10, pp. 760-779.

- (1976). Linear programming via a non-differentiable penalty function, SIAM

J. Numer. Anal. 13, pp. 145-154.

- (1979). An efficient second-order method to solve the (constrained) minimax

problem. Report CORR-79-5, University ot Waterloo. Canada.

Кони и Петшнковский

Conn A. R. and Pietrzykowski T. (1977). A penalty function method converging directly to a constrained optimum, SlAM J. Numer. Anal. 14, pp. 348-375. KoHH и Синклер

Conn A. R. and Sinclair J, W. (1975). Quadratic prtramming via a non-differentiable penalty function. Report 75/15, Department of Combinatorics and Optimization, University of Waterloo, Canada.

Корт

Kort B. W. (1975). «Rate of convergence of the method of multipliers with inexact

minimization)), in Nonlinear Prcramming 2 (O. L. Mangasarian, R. R. Meyer and S. M. Robinson, eds.), pp. 193-214, Academic Press, London and New York.

Корт и Бертсекас

Kort В. W. and Bertsekas D. P. (1976). Combined primal dual and penalty methods for convex programming, SIAM J. Control and Optimization 14, pp. 268-294.

Коттл

Cottle R. W. (1974). Manifestations of the Schur complement. Linear Algebra and its Applies. 8, pp. 189-211.

Коши

Cauchy A. (1847). Methode Generale pour la Resolution des Systems dEquations Sirnultanees, Сотр. Rend. Acad. Sci. Paris, pp. 536-538.

Kuhn H. W. (1976). ((Nonlinear programming: a historical view», in SLAM-AMS Proceedings, Volume IX, Mathematical Programming (R. C-Cottle and C. E. Lemke, eds.), pp. 1-26, American Mathematical Society, Providence, Rhode Island.

Кун и Таккер

Kuhn Н. W. and Tucker A. W. (1951). cNonlinear Programmliig», in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (J. Neyman, ed.), pp. 481-492, Berkeley, University of California Press,