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