.png){kind=icon}
.png){kind=icon}
Return
The generalized conditional gradient method for multiobjective composite optimization problems with non-monotone line search
.png){kind=icon}
PRE
AI
DOI：10.1080/10556788.2026.2640936.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We study multiobjective composite optimization problems (MOCO), where each objective function is the sum of a continuously differentiable term and a possibly non-differentiable convex function. To generalize a technique traditionally applied in scalar optimization to the multiobjective setting, we propose a generalized conditional-gradient method (ConG) also known as the Frank-Wolfe method augmented with a non-monotone line search strategy. Unlike existing approaches, which rely on monotone or Armijo rules, our method incorporates more flexible stepsize procedures, including max-type, moving average, summable, diminishing, and gap-dependent strategies. The algorithm is designed around two tunable components: a classical backtracking rule and a novel adaptive strategy that reuses previous stepsizes, reducing computational cost. We establish asymptotic convergence to Pareto-critical points under mild boundedness assumptions and derive worst-case iteration-complexity bounds of order $ \mathcal {O}(1/\varepsilon <^>2) $ O(1/epsilon 2) when the differentiable components have Lipschitz gradients matching the best known rates for scalar conditional-gradient methods. We also provide explicit bounds on the number of function and gradient evaluations required for each stepsize rule. A key technical contribution is the use of a gap function that measures stationarity without scalarization, serving both as a stopping criterion and the basis of the complexity analysis. Numerical experiments confirm the effectiveness and efficiency of the proposed method on a variety of test problems.
Keywords:
Generalized conditional gradient method
multiobjective optimization
non-monotone line search
composite problems gap function
Pareto optimality
Journal
O
IF:
1.4
Papers:
24
Citations:
0
Organization
View more organizations