Block local elimination algorithms for solving sparse discrete optimization problems

Block elimination algorithms for solving sparse discrete optimization problems are considered. The numerical example is provided. The benchmarking is done in order to define real computational capabilities of block elimination algorithms combined with SYMPHONY solver. Analysis of the results show that for sufficiently large number of blocks and small enough size of separators between the blocks for staircase integer linear programming problem the local elimination algorithms in combination with a solver for solving subproblems in blocks allow to solve such problems much faster than used solver itself for solving the whole problem. Also the capabilities of postoptimal analysis (warm starting) are considered for solving packages of integer linear programming problems for corresponding blocks.Comment: arXiv admin note: substantial text overlap with arXiv:0901.388

Distributed Primal-dual Interior-point Methods for Solving Loosely Coupled Problems Using Message Passing

In this paper, we propose a distributed algorithm for solving loosely coupled problems with chordal sparsity which relies on primal-dual interior-point methods. We achieve this by distributing the computations at each iteration, using message-passing. In comparison to already existing distributed algorithms for solving such problems, this algorithm requires far less number of iterations to converge to a solution with high accuracy. Furthermore, it is possible to compute an upper-bound for the number of required iterations which, unlike already existing methods, only depends on the coupling structure in the problem. We illustrate the performance of our proposed method using a set of numerical examples.Comment: 39 pages, 8 figures. Submitted to Optimization Methods and Softwar