Affiliation:
1. Yeshiva University, New York, New York
Abstract
Pinning down the maximum of a function in one or more variable is a basic computing problem. Without further a priori information regarding the nature of the function, of course, the problem is not feasible for computation. Thus if the function is permitted to oscillate infinitely often then no number of evaluations can give information regarding its maximum.
J. Kiefer, in his paper, treats the one-dimensional problem and shows that the correct a priori assumption regarding the function is that of “unimodality.” He then gives the complete and exact optimal procedure within this framework.
In this paper is given what the author believes is the correct a priori background for functions of several variables. (This is analogous to unimodality in one dimension.) However, there is not obtained the exactness of Kiefer's result, but rather the determination of the correct procedures to within “order of magnitude.”
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference3 articles.
1. Sequential minimax search for a maximum;KIEFER J;Proc. Amer. Math. Soc.,1953
2. GOODMAN R. Machine Program 600-239. Sylvania Electronics Needham Mass. GOODMAN R. Machine Program 600-239. Sylvania Electronics Needham Mass.
3. The centroid of a convexbody;HAMMER P.C;Proc. Amer. Math. Soc.,1951
Cited by
53 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Sparse Submodular Function Minimization;2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS);2023-11-06
2. Learning From Human Directional Corrections;IEEE Transactions on Robotics;2023-02
3. Minimizing Convex Functions with Rational Minimizers;Journal of the ACM;2022-12-19
4. Nearly Optimal Communication and Query Complexity of Bipartite Matching;2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS);2022-10
5. Subgradient ellipsoid method for nonsmooth convex problems;Mathematical Programming;2022-06-14