Constraint Aggregation Principle in Convex Optimization

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.
KEYWORDS: nonsmooth optimization, constraint aggregation, subgradient methods, polynomial algorithms, decomposition

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