Constraint Aggregation Principle in Convex Optimization

Ermoliev, Y.M., Kryazhimskiy, A.V., & Ruszczynski, A. (1995). Constraint Aggregation Principle in Convex Optimization. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-95-015

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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 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. It is shown that in case of linear programming, the method with aggregation has a polynomial complexity. Finally, application to decomposable problems is discussed.

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