Главная  Методы условной оптимизации 

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [ 80 ] [81] [82] [83]

Курант

Courant R. (1936). Differential and Integral Calculus (two volumes). Blackie. London and Glasgow.

- (1943). Variational methods for the solution of ргоЫшк of equilibrium and vibra-

tions. Bull. Amer. Math. Soc. 49, pp. 1-23.

Кэниел и Дэкс

Kaniel S. and Dax A. (1979). A modified Newtons method for unconstrained minimization, SlAM J. Numer. Anal. 16, pp. 324-331.

Кэррол

Carrol C. W. (1959). An Operations Research Approach to the Economic Optimization of a Kraft Pulping Process, Ph. D. Thesis. Institute of Paper Chemistry, Appfeton, Wisconsin.

- (1961). The created response surface technique for optimizing nonlinear restra-

ined systems, Operations Research 9, pp. 169-184.

Л aiiHCCc

Lvness J. N. (1976). «An interface probfem in numerical softwares. Proceedings of the 6th Manitoba Conference on Numerical Mathematics, pp. 251-263,

- (1977a). cHas numerical differentiation a future?* Proceedings of the 7th Mani-

toba Conference on Numerical Mathematics, pp. 107-129.

- (1977b). «Quid, quo, quadrature?* in The State of the Art in Numerical Analvsis

(D- Jacobs, ed.), pp. 535-560, Academic Press, London and New York-

Яайкесс и Молер

Lyness J. N. and Moler C. B. (1967). Numerical differentiation of analytic functions, SlAM J. Numer. Anal. 4, pp. 202-210.

Ла11несс и Сэцд

Lyness J. N. and Sande G. (1971). ENTCAF and ENTCRE: Evaluation of normalized Taylor coefficients of an analytic (unction. Comm. ACM 14, pp. 669-675.

Левенберг

Levenbem K- (1944). A method for the solution of certain problems in least squares. Quart. Appl. Math. 2. pp. 154-168.

Лемарешаль

Lemarechal C. (1975). An extension of Davidon methods to non-differentiable problems. Math. Prog. Study 3, pp. 95-109.

Лемке

Lamke C. E. (1965). Bimatrix equilibrium points and mathematicaf programming. Management Science 11, pp. 581-689.

Ленард

Lenard M- L. (1979). A computational study of active set strategies In nonlinear programming with linear constraints, Math. Prog. 16, pp. 81-97.

Ленбергер

Luenberger D. G. (1973). Introduction to Linear and Nonlinear Programming, Ad-dison-Wesley, Menlo Park, California.

- (1974). A combined penalty function and gradient projection method for nonli-

near programming, J.Opt. Th. Applies. 14. pp. 477-495.

Лнлл

Lill S. A. (1972). ((Generalization of an exact method for solving equality constrained problems to deal with inequality constramts», in Numerical Methods for Non-Linear Optimization (F. A. Loolsma, ed.), pp. 383-3§4, Academic Press, London and New York.

Лоулер

Lawler E. L. (1980). The great mathematical sputnik of 1979, University of California, Berkeley, California (February 1980).

Лоусои в Хаисон

Lawson С. L. and Hanson R.J. (1974). Solving Least-Squares Problems, Prentice-Hall, Inc., Englewood Cliffs, New Jersey. Лутсма

Lootsma F. A. (1969). Hessian matrices of penalty functions for solving constrained optimization problems. Philips Res. Repts 24, pp. 322-331.

- (1970). Boundary properties of penalty functions for constrained optimization

problems. Philips Res. Repts 3.

- (1972). «A survey of methods for solving constrained optimization problems via

unconstrained minimizations, in Numerical Methods for Non-Linear Optimization (F. A. Lootsma, ed.), pp. 313-347, .Academic Press, London and New York

Лэсдон и Уорен

Lasdon L- S. and Waren A. D. (1978). ((Generalized reduced gradient software for linearly and nonlinearly constrained problemss, in Design and Implementation of Optimization Software (H-J. Greenberg, ed.). pp. 335-362, Sijthoff and Noordhoff, Netherlands.

Лэсдон, Уорен, Джейи и Ратнер

Lasdon L. S., Waren A. D-, Jain A. and Ratner M. (1978). Design and testing of a GRG code for nonlinear optimization, ACM Trans. Math. Software, 4, pp. 34- 50.

Лэсдон, Фокс и Ратнер

Lasdon L. S., Fox R. L. and Ratner M. (1973). An efficient one-dimensional search procedure lor barrier functions, Math. Prog. 4, pp. 279-296.

Мадсен

Madsen K. (1975). An algorithm for the minimax sofution of overdetermined systems of linear equations, J. Inst. Maths. Applies. 16. pp. 321-328.

Мак-Кормик

McCormick G. P. (1969). Anti-zygzagging by bending. Management Science 15, pp. 315-320.

- (1970a). The variable reduction method for nonlinear programming. Management

Science 17, pp. 146-160.

- (1970b). (cA .second-order method for the linearly constrained nonlinear program-

ming problems, in Nonlinear Programming (J.B.Rosen, O. L-Mangasarian and K- Ritter, eds.), pp. 207-243, Academic Press. London and New York.

- (1977). A modification of Armijos step-size rule for negative curvature. Math.

Prog. 13. pp. 11-115.

Мак-Лин и Уотсон

McLean R. A. and Watson G. A. (1979). Numerical methods for nonlinear discrete /, approximation problems, proceedings of the Oberwolfach Conference on Approximation Theory (to appear).

Мангасарьян

Mangasarian O. L. (1969). Nonlinear Programming, McGraw-Hill Book Co., New York.

- (1975). Unconstrained Lagrangians in nonlinear programming, SlAM J. Control

and Optimization 13, pp. 772-791.

Маратос

ralos N . - ,

Control Optimization Problems, Ph. D. Thesis, University of London.

Maralos N- (1978). Exact Penalty Function Algorithms for Finite-Dimensional and

Марвнл

Marttil E. (1978). Exploiting Sparsity in Newton-Type Alethods, Ph. D, Thesis. Cornell University, Ithaca, New York.



Маркардт

Marquardt D. (1963), An algorithm for least-squares estimation of nonlinear parame ters. SIAM J, Appl, Math. 11, pp. 431-441.

Марковнц

Markowitz H. M, (1957). The elimination lorm of the inverse and its applications to linear programming, Management Science 3, pp. 255-269.

Марстен

Marsten R. E, (1978). XMP: A structured library of subroutmes for experimental mathematical programming. Report 351, Department of Management Information Systems, University of Arizona, Tucson. Arizona.

Марстен н Шанно

Marsten R, E. and Shanno D- F, (1979). Conjugate-gradient methods for linearly constrained nonlinearly programming. Report 79-13. Department of Management Information Systems, University of Arizona, Tucson, Arizona.

Миеле, Крэгг, Aiiep и Леви

Miele A.. Cragg E. E., Iyer R. R. and Levy A. V. (1971). Use of the augmented penalty function in mathematical programming. Part i, J.Opt. Th. Applies. 8, pp. 115-130.

Миеле, Крэгг и Леви

Miele А., Cragg Е. Е. and Levy А. V. (1971). Use of the augmented penalty function in mathematical programming. Part li, J.Opt. Th. Applies. 8, pp. 131-153,

Миллер

Miller С E. (1963). «The simplex method for focal separable programming», in Recent Advances in Mathematical Programming (R. L. Graves and P. Wolfe, eds.). pp. 89-100, McGraw-Hill Book Co., New York.

Миффлин

Mifflin R, (1975). A superlinearly convergent algorithm for minimization without evaluating derivatives. Math. Prog. 9, pp. 100-117.

- (1977). Semismooth and .semiconvex functions in constrained optimization, SIAM J, Control and Optimization f5, pp. 959-972.

Mope

More J.J. (1977). «The Levenberg-Marquardt algorithm: implementation and theory*, in Numerical Analysis (G.A.Watson, ed.), pp. 105-116, Lecture Notes in Mathematics 630. Springer-Verlag, Berlin, Heidelberg and New York.

- (1979a). On the design of optimization software. Report DAMTP 79/NA 8, Uni-

versity of Cambridge.

- (1979b). Implementation and testing of optimization softwares, in Performance

Evaluation of Numerical Software (L. D. Fosdick, ed.), pp. 253-265, North-Holland, Amsterdam.

Mope и Соренсен

More J. J. and Sorensen D. C. (1979). On the use of directions of negative curvature in a modified Newton method. Math. Prog. 15, pp. 1-20.

Murtai B. A. (1981). Advanced Linear Programming. McGraw-Hill Book Co.. New-York. (Имеется перевод: Б- Муртаф. Современное лине11Ное программирование.-М-: Мир, 1984.)

Муртаф и Сарджеь[Т

Murta В. А. and Sargent R. Н. W. (1969). «А constrained minimization method with quadratic convergences, in Optimization (R. Fletcher, ed.), pp. 215-246, Academic Press, London and New York,

Муртаф и Ссждерс

Murtagh В. A. and Saunders M. A. (1977). MINOS Users Guide, Report SOL 77-9, Department of Operations Research, Stanford University, California,

--(1980). A projected Lagrangian algorithm and Its implementation for sparse

nonlinear constraints. Report SOL 80-lR, Department of Operations Research, Stanford University, California, to appear in Math, Prog. Study on Constrained Optimization.

Мэйн и Маратос

Mayne D. Q. and Maratos N. (1979). A first-order exact penalty function algorithm for equality constrained optimization problems. Math. Prog. 16, pp. 303-324, Мэйн и Полак

Mayne D, Q. and Pofak E, (1976). Feasible direction algorithms for optimization problems with equality and inequality constraints. Math, Prog, 11, pp. 67-80, Мюррей

Murray W. (1967). «Ill-conditioning in barrier and penalty functions arising in constrained nonlinear programming, presented at the Princeton Mathematical Programming Symposium, August 14-18. 1967.

- (f959a). Constrained Optimization, Ph. D. Thesis, University of London.

- (1969b). «An algorithm for constrained minimization», in Optimization (R. Flet-

cher, ed-), pp. 247-258, Academic Press. London and New York,

- (1971a). An algorithm for finding a local minimum of an indefinite quadratic

program. Report NAC 1. National Physical Laboratory, England.

- (1971b). Analytical expressions for the eigenvalues and eigenvectors of the Hessian

matrices of barrier and penalty functions, J. Opt. Th. Applies. 7, pp. 189-196.

- (1972a). ((Second derivative methods;), in Numerical Methods for Unconstrained

Optimization (W. Murray, ed.). pp. 57-71. Academic Press, London and New York.

- (1972b). eFailure, the cau-ses and cures*, in Numerical Methods for Unconstrained

Optimization (W. Murray, ed.), pp, 107-122, Academic Press, London and New York.

- (1976). ((Constrained Optimization», in Optimization In Action (L. C. W, Dixon,

ed.), pp, 217-251, Academic Press, London and New York,

Мюррей и Овертои

Murray W. and Overton M. L. (1980a). A projected Lagrangian algorithm for nonlinear minimax optimization, SIAM J. Sci. Stat. Comput. 1, pp. 345-370,

--(1980b). A projected Lagrangian algorithm for nonlinear li optimization. Report SOL 80-4, Department of Operations Research, Stanford University, California.

Мюррей и Райт

Murray W. and Wright M. H. (1976). Efficient linear search algorithms for the logarithmic berrier function. Report SOL 76-18. Department of Operations Research, Stanford University, California.

--(1978). Projected Lagrangian methods based on the trajectories of penalty and

barrier functions. Report SOL 78-23, Department of Operations Research,Stanford University, California.

--(1980). Computation of the search direction in constrained optimization

algorithms. Report SOL 80-2, Department of Operations Research, Stanford University, to appear in Math. Prog. Study on Constrained Optimization.

Назарет

Nazareth L, (197". A conjugate-direction algorithm without line searches, J. Opt. Th. Applies. 23, pp. 373-388.

- (1979). A relationship between the BFGS and conjugate-gradient algorithms and

its implications for new algorithms, SIAM J, Numer. Anal. 16, pp. 794-800. Назарет и Носедал

Nazareth L. and Nocedal J. (1978). A study of conjugate-gradient methods. Report SOL 78-29, Department of Operations Research, Stanford University, Califor-



Нелдер н Мид

Nelder J. А- and Mead R. (1965). А simplex method for function minimization. Computer Journal 7. pp. 308-313.

Немировский A. С и Юдин Д. Б. (1979). Эффективные методы решения задач выпуклого программирования большой размерности.- Экономика и математические методы, 1979, № 2, с, 135-152.

Носедал

Nocedal J. (1980). Updating quasi-Newton matrices with limited storage. Mathematics of Computation 35, pp. 773-782. Оливер

OliverJ. (1980). An algorithm for numerical differentiation of a function of one real variable. J. Сотр. Appl. Math. 6, pp. 146-160.

Оливер и Раффхед

Oliver J. and Ruffhead A. (1975). The selection of interpolation points in nur ition, Nordisk Tidskr. Informationbehandling (BIT) 15. pp.

merical 283-

differentiation, 295. ОЛирн

OLeary D. P. (1980a). A discrete Newton afgorithm for minimizing a function of many variables. Report 910, Computer Science Center. University of Maryland, College Park, Maryland.

- (1980b). Estimating matrix condition numbers. SlAM J. Sci. Stat. Comput. 1,

pp. 205-209. Open

Oren S. S. (1974a). Self-scaling variable metric (SSVM) algorithms. Part II: implementation and experiments. Management Science 20, pp. 863-874.

- (]974b). On the selection of parameters in self-scaling variable metric algo-

rithms. Math. Prog. 7, pp. 351-367. Орен и Ленбергер

Oren S. S. and Luenberger D. G. (1974). Self-scaling variable metric (SSVM) algorithms. Part 1: criteria and sufficient conditions for scaling a class of algorithms. Management Science 20, pp. 845-862.

Open и Спедикато

Oren S. S. and Spedicato E. (1976). Optimal conditioning of self-scaling and variable

metric algorithms. Math. Prog. 10, pp. 70-90. Ортега и Рейнболдт

Ortega J. M. and Rhcinboldt W. C. (1970). Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, London and New York. (Р1меется перевод: Дж. Ортега, В. Рейнболдт. Итерационные методы решения нелинейных систем уравненнй со многими неизвестными.-М.: Мир. 1975.)

Орчард-Хейс

Orchard-Hays W. (1968). Advanced Linear Programming Computing Techniques, McGraw-Hill, New York.

- (1978a). «History of mathematical programming systems*, in Design and Imple-

mentation of Optimization Software (H. J. Greenberg, ed.), pp. 1-26, Sijthoff and Noordhoff, Netherlands.

- (1978b). «Бсоре of mathematical programmind software*, in Design and Imple-

mentation of Optimization Software (H. J. Greenberg. ed.), pp. 27-40, Sijthoff and Noordhoff, Netherlands.

- (1978c). ((Anatomy of a mathematical systems, in Design and Implementation

of Optimization Software (H. J. Greenberg, ed.), pp. 41-102, Sijthoff and Noordhoff. Netherlands,

осборн и Райан

Osborne М. R. and Ryan D- M. (1972). «A hybrid algorithm for nonl inear programm-\ng». in Numerical Methods for Non-Linear Optimization (F. A. Lootsma, ed.), PP. 395-410, Academic Press, London and New York-

Осборн и Уотсон

Osborne М. R- and Watson G, A. (1969). An algorithm for minimax approximation in the nonlinear case. Computer Journal 12, pp. 63-68.

--(1971). An algorithm for discrete nonlinear /, approximation. Computer Journal 10, pp. 172-177.

Осей

Aasen J. O. (1971). On the reduction of a symmetric matrix to tridiagonal form, Nordisk Tidskr. Informationsbehandling (BIT) II, pp. 233-242.

Паркинсои и Хатчинсон

Parkinson J. M. and Hutchinson D- (1972). cAn investigation into the efficiency of variants of the simplex methods, in Numerical Methods for Non-Linear Optimization (F. A. Lootsma, ed.), pp. 115-135, Academic Press, London and New York.

Пауэлл

Powell M. J. D. (1964). An efficient method for finding the minimum of a function of several variables without calculating derivatives, Computer Journal 7, pp. 155-162.

- (1969). «A method for nonlinear constraints in minimization problems*, in Opti-

mization (R. Fletcher, ed.), pp. 283-298, Academic Press. London and New York.

- (1970a). «A new algorithm for unconstrained optimizations, in Nonlinear Pro-

frramming (J. B. Rosen, O. L. Mangasarian and K- Ritter, eds.), pp. 31-65, Academic Press, London and New York.

- (1970b). cA hybrid method for nonlinear equations*, in Numerical Methods for

Nonlinear Algebraic Equations (P, Rabinowitz, ed.), pp. 87-114, Gordon and Breach, London.

- П971). On the convergence of the variable metric algorithm, J. Inst. Maths,

Applies 7. pp. 21-36.

- (1972). ((Problems relating to unconstrained optimizations, in Numerical Methods

lor Unconstrained Optimization (W. Murray, ed.), pp. 29-55, Academic Press. London and New York.

- (1974). Klntroductioii to constrained optimizations, in Numerical Methods for

Constrained Optimization (P. E. Gill and W.Murray, eds.), pp, 1-28, Academic Press. London and New York.

- (1975). «Convergence properties of a class of minimization algoritbmss, in Non-

linear Programming 2 (O, L. Mangasarian, R. R, Meyer and S. M. Robinson, eds.), pp. 1-27, Academic Press, London and New York.

- (1976a). «A view of unconstrained optimizations, in Optimization In Action

(L. C, W. Dixon, ed.), pp. 117-152, Academic Press, London and New Yorl<.

- (1976b). Some convergence properties of the conjugate-gradient method. Math.

Prog. II, pp, 42-49,

- (1976c). aSome global convergence properties of a variable metric algorithm with-

out exact line searches*, in SlAM-AMS Proceedings, Volume IX, Mathematical Programming (R. C. Cottle and C. E, Lemke, eds.), pp. 53-72, American Mathematical Society, Providence, Rhode Island.

- (1977a). Restart procedures lor the conjugate-gradient method. Math. Prog. f2.

[ip. 241-264.

- (1977b). A fast algorithm for nonlinearly constrained optimization calculations.

Report DAMTP 77/NA 2, University of Cambridge, England.

- (1977c). «Numerical methods tor fitting functions of two variabless, in The State

ol the Art in Numerical Analysis (D-Jacobs, ed.), pp. 563-604. Academic Press, London and New York.

- (1978). «The convergence of variable metric methods for nonlinearly constrained

optimization calculations*. In Monlinear Programming 3 (O. L-Mangasarian, R. R. Meyer and S. M. Robinson, eds.), pp. 27-63, Academic Press. London and New York.



[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [ 80 ] [81] [82] [83]

0.001