Geodesic
Optimal algorithms for integration of convex functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 2, pp. 267-277

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A best quadrature formula and an algorithm that is optimal in one step for integrating a convex function of one variable are described. It is shown that the least guaranteed error of both methods are roughly the same, though, if the behaviour of the integrated function is “not the worst”, the efficiency of the optimal algorithm can be higher. 
@article{ZVMMF_1983_23_2_a2,
     author = {I. A. Glinkin},
     title = {Optimal algorithms for integration of convex functions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {267--277},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_2_a2/}
}
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I. A. Glinkin. Optimal algorithms for integration of convex functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 2, pp. 267-277. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_2_a2/