Generalization of the Decomposition Approach to Mathematical Programming and Classical Calculus of Variations

  • Vladimir Tsurkov
Part of the Applied Optimization book series (APOP, volume 37)


In this chapter, the iterative decomposition method based on the iterative aggregated variables from various blocks is applied to the wide class of extremal problems of hierarchical nature. We consider the use of the approach for the problems of linear and quadratic programming with the block diagonal structure having arbitrary binding constraints. The same is made for finite-dimensional block separable mathematical programming problems of convex type. The constructions of the method are represented in the classical calculus of variations. Here, the main concern is the condition of optimality of the disaggregated solution and the monotonicity with respect to the functional of the iterative process.


Local Problem Duality Theorem Decomposition Approach Aggregate Variable Sufficient Optimality Condition 
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References to Chapter 2

  1. [1]
    Bittner L., Abschatzungen bei Variationsmethoden mit Hilfe Dualitatssatzen I, J. Numer. Math., 1968, vol. 11, no. 2, pp. 129–143.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Gel’fand I.M. and Fomin S.V., Variatsionnoe ischislenie (Calculus of Variations), Moscow, Fizmatgiz, 1961.Google Scholar
  3. [3]
    Gol’shtein E.G., Teoriya dvoistvennosti v matematicheskom programmirovanii i eyo prilozheniya (Duality Theory in Mathematical Programming and Its Applications), Moscow: Nauka, 1971.Google Scholar
  4. [4]
    Ioffe A.D. and Tikhomirov V.M., DvoistvennosV v zadachakh variatsionnogo ischisleniya (Duality in Problems of Calculus of Variations), Dokl. Akad. Nauk SSSR, 1968, vol. 180, no. 4, pp. 789–792.Google Scholar
  5. [5]
    Lasdon L.S., Optimizatsiya boVshikh sistem (Optimization of Large Systems), Moscow, Nauka: 1975 [Russian translation].Google Scholar
  6. [6]
    Tsurkov V.I., Dekompozitsiya na osnove aggregirovaniya dlya funktsionaVnykh sistem (Aggregation-Based Decomposition for Functional Systems), Avtom. Telemekh1980, no. 3, pp. 145–155.Google Scholar
  7. [7]
    Tsurkov V.I., Dekompozitsiya v klassicheskom variatsionnom ischislenii (Decomposition in Classical Calculus of Variations), Zh. Vych. Mat. Mat. Fiz., 1979, vol. 19, no. 6, pp. 1396–1413.MathSciNetMATHGoogle Scholar
  8. [8]
    Tsurkov V.I., Dekompozitsiya v vypuklom matematicheskom programmirovanii (Decomposition in Convex Mathematical Programming), in Computational and Applied Mathematics, vol. 28, Kiev, 1979.Google Scholar
  9. [9]
    Tsurkov V.I., Printsip decompozitsii dlya blocno-separabeVnykh sistem (Decomposition Principle for Block Separable Systems), DokL Akad. Nauk SSSR, 1979, vol. 246, no. 1, pp. 27–31.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Vladimir Tsurkov
    • 1
  1. 1.Computing CenterRussian Academy of SciencesMoscowRussia

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