Constraint aggregation principle in convex optimization

Ermoliev, Y.M., Kryazhimskiy, A.V., & Ruszczynski, A. (1997). Constraint aggregation principle in convex optimization. Mathematical Programming, Series B 353-372.

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A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single surrogate inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration continues. This general aggregation principle is incorporated into a number of specific algorithms. Convergence of the new methods is proved and speed of convergence analyzed. Next, dual interpretation of the method is provided and application to decomposable problems is discussed. Finally, a numerical illustration is given.

Item Type: Article
Uncontrolled Keywords: Nonsmooth optimization; Surrogate constraints; Subgradient methods; Decomposition
Research Programs: Dynamic Systems (DYN)
Bibliographic Reference: Mathematical Programming, Series B; 76:353-372
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:08
Last Modified: 27 Aug 2021 17:15

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