Complexity bounds for primal-dual methods minimizing the model of objective function

@article{Nesterov2018ComplexityBF,
  title={Complexity bounds for primal-dual methods minimizing the model of objective function},
  author={Y. Nesterov},
  journal={Mathematical Programming},
  year={2018},
  volume={171},
  pages={311-330}
}
  • Y. Nesterov
  • Published 2018
  • Mathematics, Computer Science
  • Mathematical Programming
We provide Frank–Wolfe ($$\equiv $$≡ Conditional Gradients) method with a convergence analysis allowing to approach a primal-dual solution of convex optimization problem with composite objective function. Additional properties of complementary part of the objective (strong convexity) significantly accelerate the scheme. We also justify a new variant of this method, which can be seen as a trust-region scheme applying to the linear model of objective function. For this variant, we prove also the… Expand
Primal-dual fast gradient method with a model
Conditional gradient type methods for composite nonlinear and stochastic optimization
  • S. Ghadimi
  • Mathematics, Computer Science
  • Math. Program.
  • 2019
Frank-Wolfe Splitting via Augmented Lagrangian Method
Inexact proximal stochastic second-order methods for nonconvex composite optimization
Model Function Based Conditional Gradient Method with Armijo-like Line Search
Model Based Conditional Gradient Method with Armijo-like Line Search
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 32 REFERENCES
Gradient methods for minimizing composite functions
  • Y. Nesterov
  • Mathematics, Computer Science
  • Math. Program.
  • 2013
Primal-dual subgradient methods for convex problems
  • Y. Nesterov
  • Computer Science, Mathematics
  • Math. Program.
  • 2009
Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization
Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets
The Complexity of Large-scale Convex Programming under a Linear Optimization Oracle
Conditional gradient algorithms for norm-regularized smooth convex optimization
Universal gradient methods for convex optimization problems
  • Y. Nesterov
  • Mathematics, Computer Science
  • Math. Program.
  • 2015
Interior-point polynomial algorithms in convex programming
A regularization of the Frank—Wolfe method and unification of certain nonlinear programming methods
  • A. Migdalas
  • Mathematics, Computer Science
  • Math. Program.
  • 1994
...
1
2
3
4
...