IND ENG 160 Lecture Notes - Lecture 4: Golden Ratio, Unimodality, The Algorithm

• School: Berkeley
• Department: Industrial Engineering And Operations Research
• Course: IND ENG 160
• Professor: Javad Lavaei

Document Summary

Unimodal: f (x) is unimodal on [a, b] if for some point x , f (x) is strictly increasing on [a, x ] and strictly decreasing on [x , b]. The structure of this algorithm is an optimization algorithm communicating with a black box solver of the function. The algorithm samples two points x1, x2 and compares their values in the function: f (x1) > f (x2): then, we know x < b. We have reduced the interval in which x may lie: f (x1) < f (x2): then, we know x > a. We have reduced the interval in which x may lie. xitem f (x1) = f (x2): then, we know x1 > x > x2. We have reduced the interval in which x may lie. Because we are continually reducing the interval in which x may lie, our. If we execute this algorithm and arbitrary number of times, we will get arbitrarily close to x .