Optimal Search for a Maximum with Sequences of Simultaneous Function Evaluations

A minimax search plan is developed for locating the maximum of a unimodal function of one variable with a sequence of blocks of simultaneous function evaluations. The proposed “block search strategy” is described for any number of simultaneous function evaluations (experiments) and for any number of blocks in the sequence. For one experiment per block it reduces to the Fibonacci strategy; in the case of only one block of experiments, to the simultaneous search plan. The “block search strategy” is optimal in the sense that for a required final interval of uncertainty, known to contain the point where the function attains its maximum, and for any given number of simultaneous experiments and blocks, it has the largest possible starting interval. A discrete variable version of the proposed search strategy is also described.

• 저널Management Science · 12(9) · 722–731
• 토픽Control Systems and Identification · Control and Systems Engineering
• DOI10.1287/mnsc.12.9.722
• 저자Mordecai Avriel, Douglass J. Wilde