Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
Random Search Method with a “Memory” for Global Extremum of a Function. / Vladimirova, Liudmila Vasilevna; Ermakov, Sergey Michaylovich.
10th International Workshop on Simulation and Statistics: Workshop booklet. Salzburg : Universitat Salzburg, 2019. p. 89.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
}
TY - GEN
T1 - Random Search Method with a “Memory” for Global Extremum of a Function
AU - Vladimirova, Liudmila Vasilevna
AU - Ermakov, Sergey Michaylovich
PY - 2019/9
Y1 - 2019/9
N2 - 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.
AB - 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.
M3 - Conference contribution
SP - 89
BT - 10th International Workshop on Simulation and Statistics
PB - Universitat Salzburg
CY - Salzburg
T2 - 10th International Workshop on Simulation and Statistics<br/>
Y2 - 2 September 2019 through 6 September 2019
ER -
ID: 48414649