Bibliography of Soviet and Western European Publications on Large-Scale Linear Programming

Dantzig, G.B., Dempster, M.A.H. and Kallio, M.J.

IIASA Collaborative PaperDecember 1984

Dantzig, G.B., Dempster, M.A.H. and Kallio, M.J. (1984) Bibliography of Soviet and Western European

Publications on Large-Scale Linear Programming. IIASA Collaborative Paper. IIASA, Laxenburg, Austria, CP-84-

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BIBLIOGRAPHY OF SOVIET AND EASIERN EWROPEAN PUBLICATIONS ON LARGE-SCALE LINEAR PROGRAMMING

G.B. Dantzig M.AH. Dempster M. Kallio Editors

December 1984 CP-84-59

Collaborative h p e r s report work which has not been performed solely a t the International Institute for Applied Systems Analysis and which has received only limited review. Views or opinions, expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work.

INTERNATIONAL INSTITUTE FOR APPLJED SYSTEMS ANALYSIS 2361 Laxenburg. Austria

This bibliography originates from the Workshop on Large-Scale Linear Programming held a t IIASA over the period June 2-6 1980. The Proceedings of this Workshop (edited by G.B. Dantzig, M.A.H. Dempster and M. Kallio, IIASA CP-81-S1) contains a bibliography covering North American and Western European publications. This bibliography is a sup- plement which covers Eastern European work on large-scale linear pro- gramming.

As some important work may still be missing, further contributions (with English translations of titles published in other languages) are most welcome. Such contributions should be sent to H . Gasking at IIASA, where a computerized bibilography is maintained. Revised versions will be issued from time to time.

This bibliography could not have been produced without the assis- tance of K. Beer, V . k Bulavski, N.K. Burova, M . h H . Dempster, M. Grauer, M. Kallio, V.E. Krivonozhko, k Propoi, M. Soismaa, B. Strazicky and R.k Zvjagina.

A.G. Aganbegjan and K.A. Bagrinovskij, "On the coordination of global and local planning problems," pp. 53-68 in P r o b l e m s in t h e Appl ica t ion o f Macroeconomic Models t o R u n n i n g , Progress, Moscow (1972). (in Russian).

P.A. Akhmetov and U.H. Malkov. "Increasing the efficiency of a multiplica- tive algorithm of simplex type in large-scale linear programming prob- lems," E k o n o m . i Matem. Metody 6, pp.422-426, (1970) (in Russian).

B.I. Alejnikov, G.Z. Davidovich, and B.S. Fomin, "A decomposition approach to external trade optimization problems," pp. 71-77 in Economic-Mathemat ical Models, Nauka, Moscow (1969) (in Russian).

M. Altman, "An elimination method for linear programming 'with applica- tion to the decomposition problem," Bull. Acad. Polon. S z i . , S r . Ski . Math., As t ron . , PRys. 13, pp.49-53 (1965).

M. Altman, "Two gradient method algorithms for linear programming with application to the decomposition problem," Bull. Acad. Polon. Sci . , S r . Ski . Math. A s t ~ o n . , W s . 13, pp.465-472 (1965).

A.A. Anikeich, A.B. Gribov, and I.V. Romanovskij, "On a transhipment route problem," Kiberne t i ka , (1965) (in Russian).

D.D. Anisimov-Spiridonov, Methods a n d Models f o r Block Q t i m a l R u n n i n g a n d Control S y s t e m s , Moscow (1969) (in Russian).

L. Aret, "On the multi-index transportation problem," I zves t i j a AN B t o n - s k o j SSR, &.-Mat 23, pp.155-159, (1974) (in Russian).

Yu.S. Arkhangel'skij, "Perfect aggregation in transportation problems." pp. 56-71 in Economic Cyberne t i c s a n d Q e r a t i o n s Research , Naukova Dumka, Kiev (1966) (in Russian).

L.A Astanina and V.A. Volkonskij, "An iterative decomposition method for the multibranch interregional model and its experimental use," ono om. i M a t e m . Metody 11. pp.83-98. (1975) (in Russian).

I. Bach, "Solution of transportation problems with additional linear con- straints," Acta R c h . Acad. Sci. Hungar . 66, pp.159-169 (1969).

I. Bach, "Solution of transportation problems with 1.ine ar constraints," pp. 75-80 in XV In t e rna t iona l Sc i en t i f i c Co l loqu ium, ,%ries Al, llrnenau ('1970) (in German).

M.M. Bachmet'ev, 1.Ya Vakhutinskij, L.M. Dudkin, V.N. Livshits, and E.I. Pozamantir, "A decomposition method for optimal planning of the national economy," pp. 74-98 in Proceed ings of t h e 4 t h Winter a h 0 0 1 o n Mathemat i - ca l P r o g r a m m i n g a n d Rela ted Prob lems , Moscow (1972) (in Russian).

AE. Bachtin, "A decomposition method for linear programming problems," pp. 63-78 in Mathemat i ca l Methods f o r Solving Economic Prob lems , Nauka, Novosibirsk (1971) (in Russian).

AE. Bachtin, "On a method for optimal distribution of resources in economic systems," pp. 29-54 in Mathemat i ca l B o b l e m s in t h e F o h a - tion of Economic Models, Nauka, Novosibirsk (1973) (in Russian).

AE. Bachtin and E.N. Zvonov. "Numerical methods for solving linear models for optimal regional production planning." pp. 97-113 in Mathemat i ca l Methods f o r Formula t ing Economic Models, Nauka, Novosi- birsk (1973) (in Russian).

A.E. Bachtin and H.F. Pastukhov, "On a composition method for the crea- tion and analysis of optimal distribution-transportation plans," pp. 62-87 in Opt imiza t ion of the Development and Distr ibut ion of Endustrial Produc- t ion , Novosibirsk (1974) (in Russian).

A.E. Bachtin, "On the implementation of the dual simplex method in large- scale linear programming problems." m t i m , Planirovanie 9, pp.15-38, (1967) (in Russian).

A.E. Bachtin and Yu.1. Volkov, "A successive improvement method for solv- ing a class of linear problems," Ekonom, i Matem. Metody 3, pp.581-567, (1967) (in Russian).

K.A. Bagrinovskij, AE. Bachtin, and E.L. Berljand, "Algorithms which search for the global optimum in economic systems with two planning levels," pp. 27-54 in Mathematical Methods for Formulat ing Economic Models, Nauka, Novosibirsk (1970) (in Russian).

K.A. Bagrinovskij, "Formulation of local problems and the distribution of resources," pp. 5-41 in Mathematical Methods for Fbrmulat ing Economic Models. Nauka. Novosibirsk (1971) (in Russian).

K.A. Bagrinovskij, AE. Bachtin, and E.L. Berljand, "Algorithms which search for the global optimum in economic systems with two planning levels," pp. 11-28 in Mathematical Methods for Formulat ing Economic Models, Nauka, Novosibirsk (1973) (in Russian).

N.E. Bajborodin. "A linear programming method based on the replacement of general constraints by two-sided constraints and its application to almost-block-structured problems," pp. 271-275 in l he 2 2 arch fo r Ez t reme Points, University of Tomsk, Tornsk (1969) (in Russian).

B. Baran-Jarosz, Z. Jankowska-Zorychta, and R. Solich, Selected Methods fo r Decomposi t ion of Linear Programming Prob lems, PWN, Warsaw (1971) (in Polish).

M.N. Barankiewicz, "Solution of the multiple-step trarlsportation probl.em through decomposition," Przeglad Sta tys t . 18, pp.129-144, (1971) (in Pol- ish).

K. Beer, "A resource allocation method in linear programming," pp. 9-30 in Proceedings of the 376 Celostatni Conference o n Mathematicul Methods in Economics, Zadov, 23-28 S p t e m b e r , 1973, Prague (1974) (in German).

K. Beer, "Decomposition of a linear optimization problem wi.th special structure," pp. 3-6 in Proceedings of t he Z l s t Enternational S c i e n t i . c Col- loqu ium, Technical University of Ilmenau (1976) (in German).

K. Beer, Methods of Large-Scale Linear Programming, VEB Deutscher Verlag der Wissenschaften, Berlin (1977) (in German).

K. Beer. "Methods of solving optimization problems with a piecewise-linear concave objective function," Wi.sse.rz~chaftl. Zeitschri f t Tech. Hochsch. R m e n a u 22. pp.108-109. (1976) (in German).

K. Beer and J. Kaschel, "Column generation in quadratic programming," Mathem. Operationsforschung u n d Stat ist ik 10, pp.179-184, (1979) (in Ger- man).

K. Beer, R. Tichatschke, and B. Schwartz, "Multiple decomposition of linear programming problems," Mathern. @erat ionsforschung u n d Siat is t ik 2, pp.95-115, (1971) (in German).

V.P. Belukhin, "A partition principle and a primal-dual method for linear dynamic problems," Zhumal Vyc. Matem. i Matem. F f z 15, (1975) (in Rus- sian).

L.V. Belyaeva, N.G. Zhurbenko, and N.Z. Shor, "On a method for solving dynamic distribution problems," ETkomm. i Matem. Metody 14, pp.137-146, (1978) (in Russian).

H. Bernau, "Upper-bound techniques for quadratic programming," in Proceedings of the 9 th h ternat iona l Mathematical Programming Sympo- sium, Budapest, Aug. 23-27, 1976, ed. A Prekopa. Hungarian Academy of Sciences.

S.I. Biryukov and AV. Shibanov, "On an algorithm which searches for bal- ance plans in a dynamic economic model," in Modelkg and Control in Developing Systems, Nauka, Moscow (1978) (in Russian).

S.I. Biryukov, "Formalized economic planning techniques IV," Avtomatika i Telemekhanika, pp.87-96, (1978) (in Russian).

S.I. Biryukov, "On a number of ways to coordinate sectoral plans," Avtoma- t M i Telemekhanika, pp. 125-1 32, (1979) (in Russian).

S.I. Biryukov and Yu.N. Ivanov, "Formalized economic planning techniques 111," Avtomatika i Te lemekhanika, pp. 113-126, (1978) (in Russian).

V . k Bolshakov, A.P. Uzdemir, and V.V. Shmelov, Problems in Banning Batch (Chtom-Mode) Production and lheir h m e r i c a l Sblution, Institute of Auto- mation and Telemechanics, Moscow (1976) (in Russian).

V . k Bolshakov, AP. Uzdemir, and V.V. Shmelov, "Problems in planning batch (custom-mode) production' and their numerical solution 111," Avtomatika i lk lemekhanika, pp.146-155, (1976) (in Russian).

G.A Borstchevskij, "On a method for solving the block programming prob- lem in computer-aided manufacturing," Ekonom. i Matem. Metody 16, pp.795-797, (1980) (in Russian).

J. Bouska and M. Cerny. "Decomposition methods in linear programming," Ekon.-Mat. Obzor 1, pp.337-369, (1965) (in Czech).

V.A. Boykov-, "On decomposition of linear functional problems 11," Avtoma- t ika i Telemekhanika, pp.106-116, (1978) (in Russian).

L.M. Bregman, "A relaxation method for finding the common point of con- vex sets and its applications in convex programming," Zhumal Vyc. Matem. i Matem. Rz. 7, pp.620-631, (1967) (in Russian).

L.M. Bregman, "An algorithm based on relaxation methods for solving con- vex programming problems," Qptim. Planirovanie 12, pp.91-94, (1969) (in Russian). L.M. Bregman, S.I. Dvorkin, and E.I. Mellech, "Optimal planning in a wire production shop," Qsledovanie Qperacij i Statisticheskos Mode lirovanie 1, pp.47-53, University of Leningrad, (1972) (in Russian).

L.M. Bregman, AN. Prygichev, and S.S. Surin, "Improvement of the efficiency of the multiplicative successive improvement method," Issledo- vanie Operacij i Statisticheskoe Modelirovanie 4, pp.3-49, University of Len- ingrad (1977) (in Russian).

AL. Brudno, "Solution of the transportation problem by the deleting numeration method," pp. 17-38 in The Use of Dig i l d Computers in Economics, Moscow (3.962) (in Russian).

V.A. Bulavski and R.A. Zvjagina, "A generalization of the block concept in linear programming," Doklady AN SSSR 235, pp.993-996, (1977) (in Russian - English translation in Sovjet Math. Dokl. 18(1977)).

V.A. Bulavski, R.k Zvjagina, and M.A. Jakovleva, NLLmerical Methods of Linear Programming, Nauka, Moscow (1977) (in Russian).

V.A. Bulavski, "An iterative method for solving the linear problem," Dok- l a d y AN SSSR 137, pp.258-260, (1961) (in Russian).

V.A. Bulavski, "An iterative method for solving the general linear pro- gram," Sibirsk. Matem. aLurn. 3, pp.313-332, (1962) (in Russian).

V.A. Bulavski, "On an algorithm for the transportation problem," Opt im. Ran i rouan ie 2, pp.41-49, (1964) (in Russian).

V.A. Bulavski, "On decomposition of the quadratic matrix into orthogonal and triangular multipliers," gibirsk. Matem. Burn. 10, pp.467-469, (1969) (in Russian).

V.A. Bulavski, "An orthogonalization method in linear programming," Opt im. Planirovanie 15, pp.7-21, (1970) (in Russian).

V . k Bulavski. "Note on the starting up of linear programming routines," Opt im. Planirovanie 15, pp.76-78, (1970) (in Russian).

V . k Bulavski, "On the solution of the special transportation problem with additional constraints," @t im izu tz i j a 1, pp.7-21, (1971) (in Russian). V.A. Bulavski. "On situations close to degenerate ones," Opt imiza tz i ja 5, pp. 5-10, (1972) (in Russian).

V.A. Bulavski. "A method of projection with regulated accuracy for convex programs," Opt im iza tz i j a 15. pp.23-31, (1974) (in Russian).

V.A. Bulavski, "Relaxation in problems involving inequalities," Optim- i z a t z i j a 23, pp.32-40, (1979) (in Russian).

V.A. Bulavski and M . k Jakovleva, "An algorithm with ordered basis for two- component linear programming problems," S o d O p t i n i z a t z i j a 36, pp.29-47, (1977) (in Russian).

V.A. Bulavski and R.k Zvjagina, "Solution of linear programming problems with branch block struct.ure matrices," Sbornik Opt imiza tz i ja 36, pp.5-28, (1977) (in Russian).

V.A. Bulavski and R.k Zvjagina, "Generalization of the block approach in l inear programming," Doklady AN SSSR 235, pp.993-996, (1977) (in Rus- sian).

V.A. Bulavski, R k Zvjagina, kk Kaplan, and V.I. Shmyrjov, "Research on numerical methods of mathematical programming," Sbornik Opt imiza tz i ja 30, (1974) (in Russian).

S.B. Bur'yan, S.S. Serov, and k P . Uzdemir, "A d.ynamic problem of industry deployment with a numerical example. Part 11," Avtomat ika i Telemekhunika. pp. 112-121, (1976) (in Russian).

S.B. Bur'yan, S.S. Serov, and k P . Uzdemir, "A dynamic problem of industry deployment with a numerical example. Part 111." Automat ika i Telemekhanika, pp. 131-138, (1976) (in Russian). S.B. Bur'yan, S.S. Serov, and AP. Uzdemir, "A method for solving the parametric problem. of finding the minimal cost in a network," Avtomat ika i Telemekhunika, pp.73-07, (1977) (in Russian).

N.P. Buslenko and G . k Sokolov, "On a class of optimal distribution prob- lems," Ekonom, i Matem. Metody 1, pp.123-136, (1965) (in Russian).

V.I. Charnyi, "On the decomposition of linear functional problems. I," Avtomat ika i Telemekhanika, pp. 116-126, (1978) (in Russian).

V.I. Curkov, "On a decomposition method based on aggregation in block programming," Zhurnal Vyc. Matem, i Matem. FZz. 19, pp.343-355, (1979) (in Russian).

V.I. Curkov, "Aggregation in branch planning problems," Ekonom. i Matem. Metody 16, pp.535-544, (1980) (in Russian).

V.I. Curkov, "An iterative decomposition method for extremal problems," DokLady AN SSR 250, pp.304-307, (1980) (in Russian).

V.I. Danilov-Danil'jan, "Block problems and iterative methods of optimal planning," in Models and Algori thms fo r @t imal Planning, Central Insti- tu te of Mathematics and Economics, Moscow (1966) (in Russian).

N.V. Djumin, "The generalized simplex method," pp. 29-33 in Operat ions Research in Computer-Aided Management (1977) (in Russian).

B.T. Dovgal', K.V. Kim, and V.A. Mas. "A method of transportation differences," B o n o m . i Matem. Metody 6, pp.92-104, (1970) (in Russian).

S.V. Dubovskij and S.S. Serov, "On the solution of the large-scale produc- tion problem," Avtomat ika i Telemekhanika, pp.121-124, (1974) (in Rus- sian).

M.S. Dubson, "A pseudoinverse matrix and i ts invariant for matrices of block-diagonal structure," Ekonom. i Matem. Metody 9, pp.361-363, (1973) (in Russian).

M.S. Dubson, "Clarification of specific properties of the matrix of con- straints in linear programming problems," Ekonom. i Matem. Metody 11. pp.395-399, (1975) (in Russian).

L.M. Dudkin and S.A. Ivanov, "Economic and geometric interpretation of the iterative aggregation process," Ekonom. i Matem. Metody 11. pp.321-329, (1975) (in Russian).

A.N. Dyukalov, Yu.N. Ivanov. A.E. Ilyutovich, V.V. Tokarev, and k P . Uzdemir, "Methods for solution of linear dynami.~ problems in economic planning," pp. 43-54 in Measurement , Control a n d Automat ion 5. CNIITE Priboros- troeniya, Moscow (1979) (in Russian).

Yu.A. Ennuste, A.incipLes of Decomposit ion Analysis in OptimaL Planning Problems, Valguz, Tallinn (1976) (in Russian).

Yu.A. Ennuste, "On a decomposition of the optimal production planning problem," Izvest i ja AN Estonskoj SSR, Obscestv. Nauki 19, pp.3-21, (1970) (in Russian).

Yu.A. Ennuste, "Decomposition analysis in optimal planning problems," Ekonom. i Matem. Metody 8, pp.535-545, (1972) (in Russian).

1.1. Eremin, "An iterative method for Chebyschev approximation of an incompatible set of linear inequalities," Doklady AN SSSR 143, pp. 1.253-1256, (1962) (in Russian).

1.1. Eremin, "Application of Feyer's approximation method to the solution of convex programming problems with nonsmooth constraints," Zhurnal Vyc. Matem. i Matem. FEZ. 9, pp. 1151-1160, (1969) (in Russian).

86. 1.1. Eremin and M.A. Kostina, "A penalty function method in linear program- ming and its computer realization," Zhumal Qc. Matem. i Matem. Fiz. ?, pp. 1358-1366, (1967) (in Russian).

87. 1.1. Eremin and V.D. Mazurov, "An iterative method for the solution of con- vex programming problems," Doklady AN SSSR 170, pp.57-60, (1966) (in Russian).

88. 1.1. Eremin and V.D. Mazurov, "Automatization of parameter control in iterative processes for mathematical programming problems," f iber- ne t ika . pp.41-46. (1979) (in Russian).

89. Yu.M. Ermoliev and L.G. Ermoleva, "A parametric decomposition method," Kibernet ika, pp.66-69, (1973) (in Russian).

90. A. Ernst, "A resource-allocation method for the solution of large-scale linear programming problems," f i senscha f t l . Zeitschri f t Tech. Hochsch. Kar l -Man-Stadt 21, pp.901-908, (1979) (in ~ e r m a n ) .

91. E.B. Ershov, "On the clarification and use of the structural features of matrices in planning problems." Ekonom. i Matem. Metody 2, pp.249-261, (1986) (in Russian).

92. Yu.M. Fatkin and V.I. Charnyi, "An iterative process for determining the optimal control in hierarchically structured systems," Avtomat ika i Telemekhunika, pp. 102-112, (1973) (in Russian).

93. Yu.A. Flerov, "Multilevel dynamic games and decentralized control," pp. 19-25 in Methods of Decentra l ized Control, Moscow (1972) (in Russian).

94. F. Forgo and J. Szep, On the A p r o z i m a t e S l u t i o n of Large-Scale Linear Programming Problems, Department of Mathematics, Karl Marx University of Economics, Budapest (1969).

95. R. Gabasov and F.M. Kirillova, Methods of Linear Programming, Minsk (1977, 1978, 1980). In three parts (in Russian).

96. A.Yu. Galata and Yu-G. Stojan, "On squeezing parallelepipeds of arbitrary size to a parallelepiped of minimal volume," Kibernet ika, pp.81-86, (1972) (in Russian).

97. M.K. Gavurin. G.S. Rubinshtein, and S.S. Surin, "On the optimal use of resources when doing several tasks of different kinds," Bibirsk. Matem. .Burn. 3, pp.481-499, (1962) (in Russian).

98. D. Gluckaufova and D. Turkova, "Some extensions of the upper-bounds method," D o n . - M a t . abzor 9, pp.423449, (1973) (in Czech).

99. E.G. Gol'stejn and D.B. Judin. New R e n d s in Linear Programming, Sove tskoe radio, Moscow (1966) (in Russian).

100. E.G. Gol'stejn, "The block programming method," Ekonom. i Matem. Metody 2, pp.82-114, (1966) (in Russian).

101. E.G. Gol'stejn, "On a general approach to the solution of linear program- ming problems of block structure," Doklady AN SSSR 166, pp.1062-1065, (1966) (in Russian).

102. E.G. Gol'stejn, "An augmented gradient; method for searching for saddle points." D o n o m . i M a t e n . Metody 8, pp.569-579, (1972) (in Russian).

103. E.G. Gol'stejn and N.V. Tret'jakov, "Modified Lagrange functions," i ikonom. i Matem. Metody 10, pp.568-591, (1974) (in Ru.ssian).

104. E.G. Gol'stejn and N.V. Tret'jakov, "On a gradient method for minimization and convex programming algorithms connected with augmented Lagrangi- ans," Ekonorn. i Matem. Metody 11, pp.730-742, (1975) (in Russian).

105. W. Grabovski, "A numerical solution of a linear programming problem using a decomposition algorithm," Przeg lad S ta t ys t . 16, pp.30 1-316, (1969) (in Czech).

106. AB. Gribov, "A solution algorithm for the cutting plane problem," Kiber- n e t i k a , pp. 110-115, (1973) (in Russian).

107. AB. Gribov and I.V. Romanovskij, "ALGOL coding of the simplex method and its variants," Qtim. Plani rovanie 12, pp.14-26, (1969) (in Russian).

108. 1. Hecko, "Revised method for direct decomposition," D o n . - M u t . Obzor 12, pp. 57-73, (1976) (in Slovak).

109. J. Hirche, "On two modifications of Williams' decomposition method," Wissenschaf t l . Zei tschr i f t HaLLe- Wit tenberg 19. pp.123-129, (1970) (in Ger- man).

110. J. Hlavacek and I. Ocka, A Paramet r i c Method f o r Two-,%age P lann ing , Eko- nomicky ustav CSAV, Prague (1978) (in Czech).

111. J. Hlavacek, "A decomposition method with reflection," Elrcon.-Mat. 0 6 z o r 10, pp.401-427, (1974) (in Czech).

112. I.V. loslovich aud Yu.M. Makarenkov, "On a method for decreasing the dimension of linear programming problems," B o n o m . i Matern. Metody 11, pp. 16-524, (1975) (in Russian).

113. Yu.P. Ivanilov and A.I. Propoi, Dynamic Linear Programming P rob lems , Moscow (1973) (in Russian).

114. Yu.P. Ivanilov and Yu.E. Malashenko, "On a method for solving dynamic linear problems," Kibernet ika. pp.42-49, (1973) (in Russian).

115. Yu.P. Ivanilov and Al. Propoi, "Duality relations for dynamic linear pro- gramming problems," Avtomat ika i B l e m e k h a n i k a , pp.100-108, (1973) (in Russian).

116. Yu.N. Ivanov. "Formalized economic planning techniques I," Av toma t i ka i TeLemekhanika, pp. 93-101, (1978) (in Russian).

117. Yu.N. Ivanov- and A.E. Ilyutovich, "Formalized economic planning tech- niques 11, " Avtomat ika i Telemekhanika, pp. 70-78, (1978) (in Russian).

118. L.V. Ivanova and N.Z. Shor. "On an iterative method for linear program- ming problems and matrix games," pp. 22-30 in m e o w of @t ima1 Solu- tions, Kiev (1969) (in Russian).

119. AG. Ivanovskij, "On a two-branch coordinated planning problem," pp. 135-137 in Control Zysterns, Moscow (1973) (in Russian).

120. M.A Jakovleva, "On the two-component linear programming problem," Optirn. Peanirovanie 2. pp. 23-40. (1964) (in Russian).

121. M.A Jakovleva, "On the extensive use of special algorithms in linear pro- gramming," Doklady AN SSSR 179, pp.1067-1069, (1968) (in Russian).

122. M.A Jakovleva, "On a transportati.on problem with bordering," Opt im- i z a t z i j a 15, pp.79-89, (1974) (in Russian).

123. M.A Jakovleva, "A general method of taking addition.al columns into account in special linear programming problems," Opt im. Plan i rovanie 15, pp.48-57, (1970) (in Russian).

124. D.B. Judin and A.D. Judin, Ez t rema l Models in Economics , Ekonomika, Mos- cow (1979) (in Russian).

125. J. Kaschel, "On computer implementations of decomposition methods in linear programming," pp. 87-90 in Prepr in ts of the C o n f e ~ e n c e o n Mathemat ica l Opt im iza t ion , 23-29 May 2979, R t t e /H iddensee, Humboldt University, Berlin (1979) (in German).

126. J. Kaschel and B. Schwartz, "Finding directions in decomposition algo- rithms," pp. 27-35 in Proceedings of the Semina r o n Non-Convent ional Opt im iza t ion P r o b l e m , Par t I , ed. J. Gutenbaum. Warsaw (1979).

127. J. Kaschel, "On the first results obtained from the computer implementa- tion of decomposition methods using PS OPSI," pp. 55-59 in Prepr in ts of the Conference o n Mathematical Opt im iza t ion , 13-19 May 2979, W t e /Hiddensee, Humboldt University, Berlin (1980) (in German).

128. J. Kaschel, "A method for resource allocation," Wissenschaf t l . Z e i t s c h ~ f t Tech. Hochsch. Ka r l -M~Tx - S a d t 19, pp.505-5 12. (1977) (in German). ,

129. Chr. Ktihler, "A method for solving linear programming problems with branch block structure matrices," pp. 600-608 in 5. Tagung u b e r Probleme u n d Methoden d e r Matherna tkchen Physik, Heft 3, Wiss. Schriftenreihe Tech. Hochsch. Karl-Marx-Stadt (1975) (in German).

130. Chr. Kohler, "A method for solving optimization problems of special struc- ture," f i senschaf t l . Zei tschr i f t Tech. Hochsch. Karl- Marz-Stadt 17, pp. 755-760, (1975) (in German).

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