On one-step worst-case optimal trisection in univariate bi-objective Lipschitz optimization

• Univariate bi-objective Lipschitz optimization is considered.
• Tolerance of the Lipschitz lower bound over an interval is generalized.
• One-step worst-case optimal interval trisection is established.

The bi-objective Lipschitz optimization with univariate objectives is considered. The concept of the tolerance of the lower Lipschitz bound over an interval is generalized to arbitrary subintervals of the search region. The one-step worst-case optimality of trisecting an interval with respect to the resulting tolerance is established. The theoretical investigation supports the previous usage of trisection in other algorithms. The trisection-based algorithm is introduced. Some numerical examples illustrating the performance of the algorithm are provided.