IIASA RepositoryPulsar Algorithms: A Class of Coarse-Grain Parallel Nonlinear Optimization AlgorithmsJ.SobczykauthorA.P.WierzbickiauthorParallel architectures of modern computers formed of processors with high computing power motivate the search for new approaches to basic computational algorithms. Another motivating force for parallelization of algorithms has been the need to solve very large scale or complex problems. However, the complexity of a mathematical programming problem is not necessarily due to its scale or dimension; thus, we should search also for new parallel computation approaches to problems that might have a moderate size but are difficult for other reasons. One of such approaches might be coarse-grained parallelization based on a parametric imbedding of an algorithm and on an allocation of resulting algorithmic phases and variants to many processors with suitable coordination of data obtained that way. Each processor performs then a phase of the algorithm -- a substantial computational task which mitigates the problems related to data transmission and coordination. The paper presents a class of such coarse-grained parallel algorithms for unconstrained nonlinear optimization, called pulsar algorithms since the approximations of an optimal solution alternatively increase and reduce their spread in subsequent iterations. The main algorithmic phase of an algorithm of this class might be either a directional search or a restricted step determination in a trust region method. This class is exemplified by a modified, parallel Newton-type algorithm and a parallel rank-one variable metric algorithm. In the latter case, a consistent approximation of the inverse of the hessian matrix based on parallel produced data is available at each iteration, while the known deficiencies of a rank-one variable metric are suppressed by a parallel implementation. Additionally, pulsar algorithms might use a parametric imbedding into a family of regularized problems in order to counteract possible effects of ill-conditioning. Such parallel algorithms result not only in an increased speed of solving a problem but also in an increased robustness with respect to various sources of complexity of the problem. Necessary theoretical foundations, outlines of various variants of parallel algorithms and the results of preliminary tests are presented.1994-08WP-94-053Monograph

For work being deposited by its own author: In self-archiving this collection of files and associated bibliographic metadata, I grant IIASA Repository the right to store them and to make them permanently available publicly for free on-line. I declare that this material is my own intellectual property and I understand that IIASA Repository does not assume any responsibility if there is any breach of copyright in distributing these files or metadata. (All authors are urged to prominently assert their copyright on the title page of their work.)

For work being deposited by someone other than its author: I hereby declare that the collection of files and associated bibliographic metadata that I am archiving at IIASA Repository) is in the public domain. If this is not the case, I accept full responsibility for any breach of copyright that distributing these files or metadata may entail.

Clicking on the deposit button indicates your agreement to these terms.