Conditional gradient method for multiobjective optimization

We analyze the conditional gradient method, also known as Frank-Wolfe method, for constrained multiobjective optimization. The constraint set is assumed to be convex and compact, and the objectives functions are assumed to be continuously differentiable. The method is considered with different strategies for obtaining the step sizes. Asymptotic convergence properties and iteration-complexity bounds with and without convexity assumptions on the objective functions are stablished. Numerical experiments are provided to illustrate the effectiveness of the method and certify the obtained theoretical results.

Automated summary

The paper analyzes the conditional gradient method, also known as the Frank-Wolfe method, for constrained multiobjective optimization. Different strategies for obtaining step sizes are considered, and asymptotic convergence properties and iteration-complexity bounds are established with and without convexity assumptions on the objective functions. Numerical experiments are provided to illustrate the effectiveness of the method and certify the obtained theoretical results.