<p>This research proposes a class of filled objective penalty functions for seeking global optimal solutions to minimax constrained optimization problems. A class of objective penalty functions is constructed to obtain the local optimal solutions. Building upon these local optimal solutions, the article introduces a class of objective penalty functions with filled properties, termed as filled penalty functions. Using these filled penalty functions, our algorithm finds a globally approximate solution in finite steps. The time complexity is also analyzed. Finally, straightforward numerical examples are provided to demonstrate the effectiveness of the proposed algorithm.</p>