Abstract
We develop four iterative algorithms for the solution of separable, convex nonlinear optimization problems with a single linear constraint and bounded variables. The design of the algorithms makes them suitable for implementation on massively parallel computers of the SIMD (i.e., Single Instruction, Multiple Data) class. The algorithms are specialized for the solution of network problems whereby the linear constraint reflects conservation of flow. Details of implementations on a Connection Machine CM-2 are reported. The numerical results indicate that all algorithms are very effective, and can solve very large problems. Three of the algorithms are also very efficient when implemented on the massively parallel system. Interestingly, the most effective algorithm (in number of steps required to solve the test problems) is the least efficient (in solution time) when implemented in parallel. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
Published Version
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