On the Optimality in General Sense for Odd-Block Search

TL;DR

This paper investigates the optimality conditions for odd-block search methods, extending classical Fibonacci search theory by exploring new optimality concepts without fixed test counts.

Contribution

It introduces a new optimality theorem for odd-block search, broadening the understanding of optimal search strategies beyond fixed test scenarios.

Findings

Established a new optimality theorem for odd-block search.

Extended classical Fibonacci search results to more general settings.

Provided theoretical foundations for optimal search without fixed test constraints.

Abstract

In his classical article[3](1953), J.Kiefer introduced the Fibonacci search as a direct optimal method. The optimality was proved under the restriction: the total number of tests is given in advance and fixed. To avoid this restriction, some different concepts of optimality were proposed and some corresponding optimal me\-thods were obtained in [1], [2], [5] and [6]. In particular, the even-block search was treated in [1]. This paper deals with the odd-block search. The main result is Theorem (1.15).