R. De Leone

Parallel successive overrelaxation methods for symmetric linear complementarity problems and linear programs

A parallel successive overrelaxation (SOR) method is proposed for the solution of the fundamental symmetric linear complementarity problem. Convergence is established under a relaxation factor which approaches the classical value of 2 for a loosely coupled problem. The parallel SOR approach is then applied to solve the symmetric linear complementarity problem associated with the least norm solution of a linear program.

Optimal allocation and binding in high-level synthesis

The authors present an integer linear program (ILP) formulation for the allocation and binding problem in high-level synthesis. Given a behavioral specification and a time-step schedule of operations, the formulation minimizes wiring and multiplexer areas. An ILP model for minimizing multiplexer and wiring areas has been mathematically formulated and optimally solved. The model handles chaining, multi-cycle operations, pipelined modules, conditional branches and trades off wiring area with resource area.<<ETX>>

Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem

Convergence is established for asynchronous parallel successive overrelaxation (SOR) algorithms for the symmetric linear complementarity problem. For the case of a strictly diagonally dominant matrix convergence is achieved for a relaxation factor interval of (0, 2] with line search, and (0, 1] without line search. Computational tests on the Sequent Symmetry S81 multiprocessor give speedup efficiency in the 43%–91% range for the cases for which convergence is established. The tests also show superiority of the asynchronous SOR algorithms over their synchronous counterparts.

Serial and parallel solution of large scale linear programs by augmented lagrangian successive overrelaxation

Serial and parallel successive overrelaxation (SOR) methods are proposed for the solution of the augmented Lagrangian formulation of the dual of a linear program. With the proposed serial version of the method we have solved linear programs with as many as 125,000 constraints and 500,000 variables in less than 72 hours on a MicroVax II. A parallel implementation of the method was carried out on a Sequent Balance 21000 multiprocessor with speedup efficiency of over 65% for problem sizes of up to 10,000 constraints, 40,000 variables and 1,400,000 nonzero matrix elements.

Optimal and heuristic algorithms for solving the binding problem

In this paper we present an optimal and a heuristic approach to solve the binding problem which occurs in high-level synthesis of digital systems. The optimal approach is based on an integer linear programming formulation. Given that such an approach is not practical for large problems, we then derive a heuristic from the ILP formulation which produces very good solutions in order of seconds. The heuristic is based on a network flow model and also considers floorplanning during the design process to minimize the interconnection area. >

Error bounds for strongly convex programs and (super)linearly convergent iterative schemes for the least 2-norm solution of linear programs

AbstractGiven an arbitrary point (x, u) inRn× R+m, we give bounds on the Euclidean distance betweenx and the unique solution

A modified auction algorithm for the shortest path problem

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Massively parallel solution of quadratic programs via successive overrelaxation

to a strongly convex program in terms of the violations of the Karush-Kuhn-Tucker conditions by the arbitrary point (x, u). These bounds are then used to derive linearly and superlinearly convergent iterative schemes for obtaining the unique least 2-norm solution of a linear program. These schemes can be used effectively in conjunction with the successive overrelaxation (SOR) methods for solving very large sparse linear programs.