A Survey of Resource Directive Decomposition in Mathematical Programming

Because of the natural way in whmh subsystems are cast into subproblems, resourcedlrectwe decomposition methods of mathematical programming problems have attracted considerable attention m recent years. A review of the speczahzed literature is presented in thin paper, where the features and drawbacks of the most representative resource-drrectlve methods are analyzed. To give an appropriate chronological and technical perspective, early general methods, such as the ones of Dantmg-Wolfe and Benders, are also included m the survey.

[1]  Warren E. Walker,et al.  Letter to the Editor - A Method for Obtaining the Optimal Dual Solution to a Linear Program Using the Dantzig-Wolfe Decomposition , 1969, Oper. Res..

[2]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[3]  Gary J. Silverman,et al.  Primal Decomposition of Mathematical Programs by Resource Allocation: II—Computational Algorithm with an Application to the Modular Design Problem , 1972 .

[4]  Peter Jennergren LINEAR PROGRAMMING PROBLEMS , 1973 .

[5]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[6]  T. Fabian,et al.  Decomposition, Pricing for Decentralization and External Economies , 1964 .

[7]  R. Wets Programming Under Uncertainty: The Equivalent Convex Program , 1966 .

[8]  George L. Nemhauser,et al.  Decomposition of linear programs by dynamic programming , 1964 .

[9]  William W. White,et al.  A Status Report on Computing Algorithms for Mathematical Programming , 1973, CSUR.

[10]  Gary J. Silverman,et al.  Primal Decomposition of Mathematical Programs by Resource Allocation: I - Basic Theory and a Direction-Finding Procedure , 1972, Oper. Res..

[11]  J. L. Sanders A Nonlinear Decomposition Principle , 1965 .

[12]  Arthur M. Geoffrion,et al.  Primal Resource-Directive Approaches for Optimizing Nonlinear Decomposable Systems , 1970, Oper. Res..

[13]  H. Mine,et al.  Decomposition of mathematical programming problems by dynamic programming and its application to block-diagonal geometric programs , 1970 .

[14]  M. R. PINOCHET Centralization and decentralization of decision-making in transportation networks , 1976, SMAP.

[15]  R. A. Sack,et al.  Factorization of Lagrange’s Expansion by Means of Exponential Generating Functions , 1966 .

[16]  A Kate Decomposition of Linear Programs by Direct Distribution , 1972 .

[17]  J. Kornai,et al.  Two-Level Planning , 1965 .

[18]  J. B. Rosen Primal partition programming for block diagonal matrices , 1964 .

[19]  J. F. Benders Partitioning procedures for solving mixed-variables programming problems , 1962 .

[20]  Harvey J. Everett Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources , 1963 .

[21]  J. B. Rosen,et al.  Solution of Nonlinear Programming Problems by Partitioning , 1963 .

[22]  Clarence Zener,et al.  Geometric Programming : Theory and Application , 1967 .