A dynamic factorization algorithm is developed which algebraically partitions the basis inverse in such a manner so that the simplex method can be executed from a series of small inverses and the basis itself. This pa...
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The safe dissemination of statistical tabular data is one of the main concerns of National Statistical Institutes (NSIs). Although each cell of the tables is made up of the aggregated information of several individual...
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The safe dissemination of statistical tabular data is one of the main concerns of National Statistical Institutes (NSIs). Although each cell of the tables is made up of the aggregated information of several individuals, the statistical confidentiality can be violated. NSIs must guarantee that no individual information can be derived from the released tables. One widely used type of methods to reduce the disclosure risk is based on the perturbation of the cell values. We consider a new controlled perturbation method which, given a set of tables to be protected, finds the closest safe ones - thus reducing the information loss while preserving confidentiality. This approach means solving a quadratic optimization problem with a much larger number of variables than constraints. Real instances can provide problems with millions of variables. We show that interior-point methods are an effective choice for that model, and, also, that specialized algorithms which exploit the problem structure can be faster than state-of-the art general solvers. Computational results are presented for instances of up to 1000000 variables.
A proximal bundle methcxi is presented for minimizing a nonsmooth convex function f. At each iteration it requires only one approximate evaluation of f and its £-subgradient, and finds a search direction via quad...
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A proximal bundle methcxi is presented for minimizing a nonsmooth convex function f. At each iteration it requires only one approximate evaluation of f and its £-subgradient, and finds a search direction via quadratic programming. When applied to Lagrangian decomposition of convex programs, it allows for inexact solutions of decomposed subproblems; yet, increasing their required accuracy automatically, it asymptotically ftnds both primal and dual solutions. Some encouraging numerical experience is reported.
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