1489:
70:
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high accuracy. A novel approach to optimize the HOG algorithm parameters and image size for facial recognition using a Tree-structured Parzen
Estimator (TPE) based Bayesian optimization technique has been proposed. This optimized approach has the potential to be adapted for other computer vision applications and contributes to the ongoing development of hand-crafted parameter-based feature extraction algorithms in computer vision.
447:
Bayesian
Optimization has been applied in the field of facial recognition. The performance of the Histogram of Oriented Gradients (HOG) algorithm, a popular feature extraction method, heavily relies on its parameter settings. Optimizing these parameters can be challenging but crucial for achieving
349:
problems. Optimization problems can become exotic if it is known that there is noise, the evaluations are being done in parallel, the quality of evaluations relies upon a tradeoff between difficulty and accuracy, the presence of random environmental conditions, or if the evaluation involves
300:
over the objective function. The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines the next query point.
1058:
Kent, Paul; Gaier, Adam; Mouret, Jean-Baptiste; Branke, Juergen (2023-07-19). "BOP-Elites, a
Bayesian Optimisation Approach to Quality Diversity Search with Black-Box descriptor functions".
1386:
401:
205:
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The maximum of the acquisition function is typically found by resorting to discretization or by means of an auxiliary optimizer. Acquisition functions are maximized using a
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over it. The prior captures beliefs about the behavior of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the
120:
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140:
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A Tutorial on
Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
384:
so as to minimize the number of function queries. As such, Bayesian optimization is well suited for functions that are expensive to evaluate.
1250:
1106:
913:
Proceedings of the 9th
International Conference on Information Processing in Sensor Networks, IPSN 2010, April 12–16, 2010, Stockholm, Sweden
659:
556:
34:
functions, that does not assume any functional forms. It is usually employed to optimize expensive-to-evaluate functions. With the rise of
73:
Bayesian optimization of a function (black) with
Gaussian processes (purple). Three acquisition functions (blue) are shown at the bottom.
1956:
1418:
986:
947:
304:
There are several methods used to define the prior/posterior distribution over the objective function. The most common two methods use
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1331:
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Mohammed Mehdi
Bouchene: Bayesian Optimization of Histogram of Oriented Gradients (Hog) Parameters for Facial Recognition. SSRN (2023)
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529:
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1987:
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to construct two distributions for 'high' and 'low' points, and then finds the location that maximizes the expected improvement.
603:
1982:
960:
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1934:
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A Bayesian exploration-exploitation approach for optimal online sensing and planning with a visually guided mobile robot
497:
477:
207:), and whose membership can easily be evaluated. Bayesian optimization is particularly advantageous for problems where
1977:
1919:
1544:
256:, is continuous and takes the form of some unknown structure, referred to as a "black box". Upon its evaluation, only
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1604:
1992:
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Since the objective function is unknown, the
Bayesian strategy is to treat it as a random function and place a
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35:
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754:: Portfolio Allocation for Bayesian Optimization. Uncertainty in Artificial Intelligence: 327–336 (2011)
61:
and is coined in his work from a series of publications on global optimization in the 1970s and 1980s.
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627:
Proceedings of the 20th
International Conference on Artificial Intelligence and Statistics, PMLR
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1350:
1211:
Constrained
Bayesian Optimization for Automatic Chemical Design using Variational Autoencoders
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1163:
1102:
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AI-optimized detector design for the future Electron-Ion Collider: the dual-radiator RICH case
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Hyperopt: A Python Library for Optimizing the Hyperparameters of Machine Learning Algorithms
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884:. Ann. Math. Artif. Intell. Volume 76, Issue 1, pp 5-23 (2016) DOI:10.1007/s10472-015-9463-9
751:
675:
MoÄŤkus, Jonas (1977). "On Bayesian Methods for Seeking the Extremum and their Application".
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441:
413:
322:
305:
39:
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Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting
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Auto-WEKA: combined selection and hyperparameter optimization of classification algorithms
854:
Ruben Martinez-Cantin, Nando de Freitas, Eric Brochu, Jose Castellanos and Arnaud Doucet.
842:
425:
69:
1093:. GECCO '23. New York, NY, USA: Association for Computing Machinery. pp. 1019–1026.
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Automatic Chemical Design using a Data-Driven Continuous Representation of Molecules
1183:
871:. International Journal of Robotics Research, volume 32, number 7, pp 806–825 (2013)
868:
444:, quality-diversity optimization, chemistry, material design, and drug development.
345:
being easy to evaluate, and problems that deviate from this assumption are known as
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1358:
239:
145:
125:
38:
innovation in the 21st century, Bayesian optimizations have found prominent use in
623:"Fast bayesian optimization of machine learning hyperparameters on large datasets"
622:
1081:
56:
1939:
1321:
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is difficult to evaluate due to its computational cost. The objective function,
1018:
1002:
Safe Exploration in Reinforcement Learning: Theory and Applications in Robotics
822:. ACM Transactions on Graphics, Volume 39, Issue 4, pp.88:1–88:12 (2020). DOI:
806:. ACM Transactions on Graphics, Volume 36, Issue 4, pp.48:1–48:11 (2017). DOI:
286:
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650:
642:
Optimization Techniques IFIP Technical Conference Novosibirsk, July 1–7, 1974
1098:
920:
790:
163:
31:
1175:
1132:"Data-Efficient Design Exploration through Surrogate-Assisted Illumination"
845:. International Joint Conference on Artificial Intelligence: 944–949 (2007)
791:
A Bayesian Interactive Optimization Approach to Procedural Animation Design
412:
The approach has been applied to solve a wide range of problems, including
823:
807:
1341:
1158:
1131:
804:
Sequential Line Search for Efficient Visual Design Optimization by Crowds
421:
1661:
935:
Sequential model-based optimization for general algorithm configuration
893:
Niranjan Srinivas, Andreas Krause, Sham M. Kakade, Matthias W. Seeger:
717:
Frazier, Peter I. (2018-07-08). "A Tutorial on Bayesian Optimization".
462:
309:
1130:
Gaier, Adam; Asteroth, Alexander; Mouret, Jean-Baptiste (2018-09-01).
640:
MoÄŤkus, Jonas (1975). "On bayesian methods for seeking the extremum".
950:. Advances in Neural Information Processing Systems: 2951-2959 (2012)
880:
Roberto Calandra, André Seyfarth, Jan Peters, and Marc P. Deisenroth
741:. Advances in Neural Information Processing Systems: 2546–2554 (2011)
644:. Lecture Notes in Computer Science. Vol. 27. pp. 400–404.
1148:
1064:
1032:
819:
780:. Advances in Neural Information Processing Systems: 409-416 (2007)
723:
1087:
Proceedings of the Genetic and Evolutionary Computation Conference
973:
972:
Chris Thornton, Frank Hutter, Holger H. Hoos, Kevin Leyton-Brown:
834:
Daniel J. Lizotte, Tao Wang, Michael H. Bowling, Dale Schuurmans:
764:
1082:"Bayesian Quality Diversity Search with Interactive Illumination"
907:
Garnett, Roman; Osborne, Michael A.; Roberts, Stephen J. (2010).
897:. IEEE Transactions on Information Theory 58(5):3250–3265 (2012)
608:
Advances in Neural Information Processing Systems 25 (NIPS 2012)
604:"Practical Bayesian Optimization of Machine Learning Algorithms"
77:
Bayesian optimization is typically used on problems of the form
1896:
1712:
1575:
1503:
1289:
1239:
911:. In Abdelzaher, Tarek F.; Voigt, Thiemo; Wolisz, Adam (eds.).
987:
Practical Bayesian Optimization of Machine Learning Algorithms
948:
Practical Bayesian Optimization of Machine Learning Algorithms
820:
Sequential Gallery for Interactive Visual Design Optimization
1487:
836:
Automatic Gait Optimization with Gaussian Process Regression
436:, planning, visual attention, architecture configuration in
1035:. 2017 JINST 12 P04028. DOI: 10.1088/1748-0221/12/04/P04028
802:
Yuki Koyama, Issei Sato, Daisuke Sakamoto, Takeo Igarashi:
546:
933:
Frank Hutter, Holger Hoos, and Kevin Leyton-Brown (2011).
882:
Bayesian optimization for learning gaits under uncertainty
1048:
2020 JINST 15 P05009. DOI: 10.1088/1748-0221/15/05/P05009
989:. Advances in Neural Information Processing Systems, 2012
858:. Autonomous Robots. Volume 27, Issue 2, pp 93–103 (2009)
1200:. ACS Central Science, Volume 4, Issue 2, 268-276 (2018)
371:
upper confidence bounds (UCB) or lower confidence bounds
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Jasper Snoek, Hugo Larochelle and Ryan Prescott Adams.
262:
242:
213:
172:
148:
128:
83:
325:
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Scott Kuindersma, Roderic Grupen, and Andrew Barto.
778:
Active Preference Learning with Discrete Choice Data
572:
Hennig, P.; Osborne, M. A.; Kersting, H. P. (2022).
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1033:Event generator tuning using Bayesian optimization
737:J. S. Bergstra, R. Bardenet, Y. Bengio, B. KĂ©gl:
337:
277:
248:
228:
199:
154:
134:
114:
869:Variable Risk Control via Stochastic Optimization
909:"Bayesian optimization for sensor set selection"
581:. Cambridge University Press. pp. 243–278.
319:Standard Bayesian optimization relies upon each
85:
42:problems, for optimizing hyperparameter values.
1225:
1223:
1221:
1219:
793:. Symposium on Computer Animation 2010: 103–112
776:Eric Brochu, Nando de Freitas, Abhijeet Ghosh:
1251:
789:Eric Brochu, Tyson Brochu, Nando de Freitas:
763:Eric Brochu, Vlad M. Cora, Nando de Freitas:
162:, which rely upon less (or equal to) than 20
8:
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739:Algorithms for Hyper-Parameter Optimization
358:Examples of acquisition functions include
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1080:Kent, Paul; Branke, Juergen (2023-07-12).
1031:Philip Ilten, Mike Williams, Yunjie Yang.
959:J. Bergstra, D. Yamins, D. D. Cox (2013).
402:Broyden–Fletcher–Goldfarb–Shanno algorithm
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380:and hybrids of these. They all trade-off
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312:. Another less expensive method uses the
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88:
82:
1492:Optimization computes maxima and minima.
818:Yuki Koyama, Issei Sato, Masataka Goto:
522:Bayesian Approach to Global Optimization
440:, static program analysis, experimental
68:
937:, Learning and Intelligent Optimization
824:https://doi.org/10.1145/3386569.3392444
808:https://doi.org/10.1145/3072959.3073598
509:
1005:(Doctoral Thesis thesis). ETH Zurich.
200:{\textstyle \mathbb {R} ^{d},d\leq 20}
1688:Principal pivoting algorithm of Lemke
946:J. Snoek, H. Larochelle, R. P. Adams
428:, automatic algorithm configuration,
7:
1213:Chemical Science: 11, 577-586 (2020)
712:
710:
708:
50:The term is generally attributed to
1332:Successive parabolic interpolation
493:Active learning (machine learning)
16:Statistical optimization technique
14:
1652:Projective algorithm of Karmarkar
750:Matthew W. Hoffman, Eric Brochu,
693:ParBayesianOptimization R package
400:or quasi-Newton methods like the
1647:Ellipsoid algorithm of Khachiyan
1550:Sequential quadratic programming
1387:Broyden–Fletcher–Goldfarb–Shanno
394:numerical optimization technique
115:{\textstyle \max _{x\in A}f(x)}
1605:Reduced gradient (Frank–Wolfe)
551:. Cambridge University Press.
524:. Dordrecht: Kluwer Academic.
272:
266:
223:
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109:
103:
1:
1935:Spiral optimization algorithm
1555:Successive linear programming
690:Wilson, Samuel (2019-11-22),
1673:Simplex algorithm of Dantzig
1545:Augmented Lagrangian methods
498:Multi-objective optimization
478:Bayesian experimental design
382:exploration and exploitation
347:exotic Bayesian optimization
767:. CoRR abs/1012.2599 (2010)
2009:
999:Berkenkamp, Felix (2019).
430:automatic machine learning
362:probability of improvement
1952:
1905:
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1876:Push–relabel maximum flow
1721:
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1678:Revised simplex algorithm
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915:. ACM. pp. 209–219.
1401:Symmetric rank-one (SR1)
1382:Berndt–Hall–Hall–Hausman
1196:Gomez-Bombarelli et al.
1136:Evolutionary Computation
1044:Evaristo Cisbani et al.
1011:10.3929/ethz-b-000370833
651:10.1007/3-540-07165-2_55
368:Bayesian expected losses
1988:Stochastic optimization
1925:Parallel metaheuristics
1733:Approximation algorithm
1444:Powell's dog leg method
1396:Davidon–Fletcher–Powell
1292:Unconstrained nonlinear
1099:10.1145/3583131.3590486
921:10.1145/1791212.1791238
545:Garnett, Roman (2023).
36:artificial intelligence
1983:Sequential experiments
1910:Evolutionary algorithm
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602:Snoek, Jasper (2012).
575:Probabilistic Numerics
483:Probabilistic numerics
434:reinforcement learning
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338:{\displaystyle x\in A}
298:posterior distribution
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1683:Criss-cross algorithm
1506:Constrained nonlinear
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1312:Golden-section search
621:Klein, Aaron (2017).
548:Bayesian Optimization
354:Acquisition functions
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314:Parzen-Tree Estimator
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20:Bayesian optimization
1600:Cutting-plane method
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365:expected improvement
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285:is observed and its
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142:is a set of points,
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1930:Simulated annealing
1748:Integer programming
1738:Dynamic programming
1578:Convex optimization
1439:Levenberg–Marquardt
1019:20.500.11850/370833
976:. KDD 2013: 847–855
963:. Proc. SciPy 2013.
520:MoÄŤkus, J. (1989).
473:Global optimization
420:and visual design,
308:in a method called
289:are not evaluated.
28:global optimization
1978:Sequential methods
1610:Subgradient method
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1419:Conjugate gradient
1327:Nelder–Mead method
841:2017-08-12 at the
458:Multi-armed bandit
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1108:979-8-4007-0119-1
661:978-3-540-07165-5
558:978-1-108-42578-0
468:Thompson sampling
418:computer graphics
375:Thompson sampling
278:{\textstyle f(x)}
229:{\textstyle f(x)}
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1335:
1334:
1329:
1324:
1319:
1314:
1308:
1306:
1296:
1295:
1290:
1283:
1282:
1265:
1263:
1262:
1255:
1248:
1240:
1232:
1231:
1215:
1202:
1189:
1142:(3): 381–410.
1122:
1107:
1072:
1050:
1037:
1024:
991:
978:
965:
952:
939:
926:
899:
886:
873:
860:
847:
827:
811:
795:
782:
769:
756:
743:
730:
704:
682:
667:
660:
632:
613:
594:
588:978-1107163447
587:
564:
557:
537:
530:
508:
507:
505:
502:
501:
500:
495:
490:
488:Pareto optimum
485:
480:
475:
470:
465:
460:
453:
450:
409:
406:
389:
386:
378:
377:
372:
369:
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334:
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274:
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249:{\textstyle f}
245:
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196:
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155:{\textstyle x}
151:
135:{\textstyle A}
131:
111:
108:
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97:
94:
91:
87:
66:
63:
47:
44:
15:
13:
10:
9:
6:
4:
3:
2:
2005:
1994:
1991:
1989:
1986:
1984:
1981:
1979:
1976:
1975:
1973:
1958:
1955:
1954:
1951:
1941:
1938:
1936:
1933:
1931:
1928:
1926:
1923:
1921:
1918:
1916:
1915:Hill climbing
1913:
1911:
1908:
1907:
1904:
1900:
1895:
1891:
1877:
1874:
1872:
1869:
1867:
1864:
1862:
1859:
1858:
1856:
1854:
1853:Network flows
1850:
1840:
1837:
1835:
1832:
1828:
1825:
1824:
1823:
1820:
1819:
1817:
1815:
1814:Shortest path
1811:
1801:
1798:
1796:
1793:
1791:
1788:
1787:
1785:
1783:
1782:spanning tree
1777:
1774:
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1766:
1758:
1754:
1751:
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1749:
1746:
1744:
1741:
1739:
1736:
1734:
1731:
1730:
1728:
1724:
1720:
1716:
1715:Combinatorial
1711:
1707:
1689:
1686:
1684:
1681:
1679:
1676:
1674:
1671:
1670:
1668:
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1570:
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1432:
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1427:
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1417:
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1412:
1411:Other methods
1408:
1402:
1399:
1397:
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1379:
1377:
1375:
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1256:
1254:
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1220:
1216:
1212:
1206:
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1199:
1193:
1190:
1185:
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1177:
1173:
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1165:
1160:
1155:
1150:
1145:
1141:
1137:
1133:
1126:
1123:
1118:
1114:
1110:
1104:
1100:
1096:
1089:
1088:
1083:
1076:
1073:
1066:
1061:
1054:
1051:
1047:
1041:
1038:
1034:
1028:
1025:
1020:
1016:
1012:
1008:
1004:
1003:
995:
992:
988:
982:
979:
975:
969:
966:
962:
956:
953:
949:
943:
940:
936:
930:
927:
922:
918:
914:
910:
903:
900:
896:
890:
887:
883:
877:
874:
870:
864:
861:
857:
851:
848:
844:
840:
837:
831:
828:
825:
821:
815:
812:
809:
805:
799:
796:
792:
786:
783:
779:
773:
770:
766:
760:
757:
753:
747:
744:
740:
734:
731:
725:
720:
713:
711:
709:
705:
695:
694:
686:
683:
678:
677:IFIP Congress
671:
668:
663:
657:
652:
647:
643:
636:
633:
628:
624:
617:
614:
609:
605:
598:
595:
590:
584:
577:
576:
568:
565:
560:
554:
550:
549:
541:
538:
533:
531:0-7923-0115-3
527:
523:
516:
514:
510:
503:
499:
496:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
464:
461:
459:
456:
455:
451:
449:
445:
443:
439:
438:deep learning
435:
431:
427:
423:
419:
415:
407:
405:
403:
399:
395:
387:
385:
383:
376:
373:
370:
367:
364:
361:
360:
359:
353:
351:
350:derivatives.
348:
332:
329:
326:
317:
315:
311:
307:
302:
299:
295:
290:
288:
269:
263:
243:
220:
214:
194:
191:
188:
185:
180:
165:
149:
129:
106:
100:
95:
92:
89:
71:
64:
62:
58:
53:
45:
43:
41:
37:
33:
29:
26:strategy for
25:
21:
1920:Local search
1866:Edmonds–Karp
1822:Bellman–Ford
1592:minimization
1424:Gauss–Newton
1374:Quasi–Newton
1359:Trust region
1267:Optimization
1205:
1192:
1139:
1135:
1125:
1086:
1075:
1053:
1040:
1027:
1001:
994:
981:
968:
955:
942:
929:
912:
902:
889:
876:
863:
850:
830:
814:
798:
785:
772:
759:
746:
733:
697:, retrieved
692:
685:
676:
670:
641:
635:
626:
616:
607:
597:
574:
567:
547:
540:
521:
446:
411:
408:Applications
391:
379:
357:
346:
318:
303:
291:
76:
52:Jonas Mockus
49:
19:
18:
1940:Tabu search
1351:Convergence
1322:Line search
432:toolboxes,
287:derivatives
55: [
1972:Categories
1771:algorithms
1279:heuristics
1271:Algorithms
1149:1806.05865
1065:2307.09326
724:1807.02811
699:2019-12-12
679:: 195–200.
629:: 528–536.
504:References
396:, such as
164:dimensions
1726:Paradigms
1625:quadratic
1342:Gradients
1304:Functions
1168:1063-6560
1117:259833672
330:∈
192:≤
93:∈
32:black-box
1957:Software
1834:Dijkstra
1665:exchange
1463:Hessians
1429:Gradient
1184:47003986
1176:29883202
839:Archived
452:See also
422:robotics
122:, where
65:Strategy
1800:Kruskal
1790:BorĹŻvka
1780:Minimum
1517:General
1275:methods
463:Kriging
310:kriging
46:History
1662:Basis-
1620:Linear
1590:Convex
1434:Mirror
1391:L-BFGS
1277:, and
1182:
1174:
1166:
1115:
1105:
658:
585:
555:
528:
1861:Dinic
1769:Graph
1180:S2CID
1144:arXiv
1113:S2CID
1091:(PDF)
1060:arXiv
719:arXiv
579:(PDF)
294:prior
59:]
22:is a
1827:SPFA
1795:Prim
1389:and
1172:PMID
1164:ISSN
1103:ISBN
656:ISBN
583:ISBN
553:ISBN
526:ISBN
1757:cut
1622:and
1154:doi
1095:doi
1015:hdl
1007:doi
917:doi
646:doi
86:max
30:of
1974::
1273:,
1269::
1218:^
1178:.
1170:.
1162:.
1152:.
1140:26
1138:.
1134:.
1111:.
1101:.
1084:.
1013:.
707:^
654:.
625:.
606:.
512:^
424:,
416:,
404:.
195:20
57:lt
1755:/
1259:e
1252:t
1245:v
1186:.
1156::
1146::
1119:.
1097::
1068:.
1062::
1021:.
1017::
1009::
923:.
919::
727:.
721::
664:.
648::
610:.
591:.
561:.
534:.
333:A
327:x
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270:x
267:(
264:f
244:f
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221:x
218:(
215:f
189:d
186:,
181:d
176:R
166:(
150:x
130:A
110:)
107:x
104:(
101:f
96:A
90:x
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