Random Search Method with a “Memory” for Global Extremum of a Function

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review


The general scheme of stochastic global optimization methods can be represented as fol-lows. In the regionDof extremum search for the functionf(X),NpointsXj(j=1,...,N) are chosen randomly or quasi-randomly andNvaluesf(Xj) are calculated. OftheNpoints,mpoints are stored, wherefvalues are the largest (smallest). The set ofthese m points is called the zero generation. After this, the iterative Markov algorithmis executed. If thek-th generation ofmkpoints is determined, the method is specified toof obtain the (k+ 1)-th generation ofmk+1points. The methods mentioned provide thesequence of generations to converge with probability 1 to the global extremum point.Our report discusses one of methods of this kind proposed by the authors in 1977.The proposed method idea is to construct the normal density on the basis ofk-th genera-tion points. The points of the next generation are sampled from the normal distribution.The number of points decreases withkgrowth. On final stages it is advisable to use thegradient method.Random extremum search with covariance matrix (search with ”memory”) is convenientfor solving problems of charged beam dynamics optimization. Such problems are dedi-cated to minimization of quality functional by control parameters.
Original languageEnglish
Title of host publication10th International Workshop on Simulation and Statistics
Subtitle of host publicationWorkshop booklet
Place of PublicationSalzburg
PublisherUniversitat Salzburg
StatePublished - Sep 2019
Event10th International Workshop on Simulation and Statistics
- Salzburg, Australia
Duration: 2 Sep 20196 Sep 2019


Conference10th International Workshop on Simulation and Statistics
Internet address

Scopus subject areas

  • Mathematics(all)


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