Open-ended status of Problem 5: maximizing monotone weakly-submodular functions under two matroid constraints

Develop a mathematically rigorous approximation algorithm for maximizing a non-negative monotone γ-weakly-submodular set function f:2^N→R under the intersection of two matroid constraints M1=(N,I1) and M2=(N,I2), with a provable approximation guarantee; formulate and assess a clear conjecture describing the attainable ratio, as the problem currently lacks a concrete conjecture and remains unsolved.

Background

Problem 5 asks for maximizing a non-negative monotone γ-weakly-submodular function subject to two matroid constraints. The authors initially expected an easy extension of known single-matroid results but, after interactions with GPT-5, found the analysis more challenging than anticipated.

They explicitly state that they presently lack a clear conjecture for this problem and that it remains open-ended, awaiting a solution.