Constraint aggregation principle in convex optimization |
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Authors: | Yuri M Ermoliev Arkadii V Kryazhimskii Andrzej Ruszczyński |
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Institution: | (1) International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria |
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Abstract: | 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. |
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Keywords: | Nonsmooth optimization Surrogate constraints Subgradient methods Decomposition |
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