@techreport{iiasa4577, month = {February}, type = {IIASA Working Paper}, title = {Constraint Aggregation Principle in Convex Optimization}, address = {IIASA, Laxenburg, Austria}, publisher = {WP-95-015}, year = {1995}, url = {https://pure.iiasa.ac.at/id/eprint/4577/}, 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.}, author = {Ermoliev, Y. M. and Kryazhimskiy, A. V. and Ruszczynski, A.} }