?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4158%2F&rft.title=Pulsar+Algorithms%3A+A+Class+of+Coarse-Grain+Parallel+Nonlinear+Optimization+Algorithms&rft.creator=Sobczyk%2C+J.&rft.creator=Wierzbicki%2C+A.P.&rft.description=Parallel+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%2C+the+complexity+of+a+mathematical+programming+problem+is+not+necessarily+due+to+its+scale+or+dimension%3B+thus%2C+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%2C+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%2C+parallel+Newton-type+algorithm+and+a+parallel+rank-one+variable+metric+algorithm.+In+the+latter+case%2C+a+consistent+approximation+of+the+inverse+of+the+hessian+matrix+based+on+parallel+produced+data+is+available+at+each+iteration%2C+while+the+known+deficiencies+of+a+rank-one+variable+metric+are+suppressed+by+a+parallel+implementation.+Additionally%2C+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%2C+outlines+of+various+variants+of+parallel+algorithms+and+the+results+of+preliminary+tests+are+presented.&rft.publisher=WP-94-053&rft.date=1994-08&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4158%2F1%2FWP-94-053.pdf&rft.identifier=++Sobczyk%2C+J.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F2404.html%3E+%26+Wierzbicki%2C+A.P.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1663.html%3E++(1994).++Pulsar+Algorithms%3A+A+Class+of+Coarse-Grain+Parallel+Nonlinear+Optimization+Algorithms.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-94-053+++++