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.

中文翻译：

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多目标优化的条件梯度法

我们分析了条件梯度法，也称为Frank-Wolfe方法，用于约束多目标优化。约束集被假定为凸且紧凑的，目标函数被假定为可连续微分。考虑该方法具有用于获得步长的不同策略。建立了目标函数的渐近收敛性和迭代复杂性边界（带或不带凸假设）。数值实验证明了该方法的有效性，并验证了所获得的理论结果。