Generalization of the Decomposition Approach to Mathematical Programming and Classical Calculus of Variations
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.
Unable to display preview. Download preview PDF.
References to Chapter 2
- Gel’fand I.M. and Fomin S.V., Variatsionnoe ischislenie (Calculus of Variations), Moscow, Fizmatgiz, 1961.Google Scholar
- 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
- 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
- Lasdon L.S., Optimizatsiya boVshikh sistem (Optimization of Large Systems), Moscow, Nauka: 1975 [Russian translation].Google Scholar
- 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
- Tsurkov V.I., Dekompozitsiya v vypuklom matematicheskom programmirovanii (Decomposition in Convex Mathematical Programming), in Computational and Applied Mathematics, vol. 28, Kiev, 1979.Google Scholar