scholarly journals Local Convergence of Exact and Inexact Augmented Lagrangian Methods under the Second-Order Sufficient Optimality Condition

2012 ◽  
Vol 22 (2) ◽  
pp. 384-407 ◽  
Author(s):  
D. Fernández ◽  
M. V. Solodov
Keyword(s):  
Optimality Condition ◽  
Local Convergence ◽  
Augmented Lagrangian ◽  
Second Order ◽  
Sufficient Optimality Condition ◽  
Augmented Lagrangian Methods ◽  
Lagrangian Methods

scholarly journals On Augmented Lagrangian Methods with General Lower-Level Constraints

2008 ◽  
Vol 18 (4) ◽  
pp. 1286-1309 ◽  
Author(s):  
R. Andreani ◽  
E. G. Birgin ◽  
J. M. Martínez ◽  
M. L. Schuverdt
Keyword(s):  
Augmented Lagrangian ◽  
Augmented Lagrangian Methods ◽  
Lagrangian Methods

scholarly journals Optimal partial transport problem with Lagrangian costs

2018 ◽  
Vol 52 (5) ◽  
pp. 2109-2132 ◽  
Author(s):  
Noureddine Igbida ◽  
Van Thanh Nguyen
Keyword(s):  
Variational Problem ◽  
Optimality Condition ◽  
Jacobi Equation ◽  
Augmented Lagrangian ◽  
Mean Field ◽  
Transport Problem ◽  
Mean Field Games ◽  
Augmented Lagrangian Methods ◽  
Need To Evaluate ◽  
Hamilton Jacobi Equation

We introduce a dual dynamical formulation for the optimal partial transport problem with Lagrangian costs cL(x,y) := ξ∈Lip([0,1];ℝN)inf {∫01 L(ξ(t), ξ˙(t))dt : ξ(0) = x, ξ(1) = y} based on a constrained Hamilton–Jacobi equation. Optimality condition is given that takes the form of a system of PDEs in some way similar to constrained mean field games. The equivalent formulations are then used to give numerical approximations to the optimal partial transport problem via augmented Lagrangian methods. One of advantages is that the approach requires only values of L and does not need to evaluate cL(x, y), for each pair of endpoints x and y, which comes from a variational problem. This method also provides at the same time active submeasures and the associated optimal transportation.

scholarly journals Adaptive augmented Lagrangian methods: algorithms and practical numerical experience

2015 ◽  
Vol 31 (1) ◽  
pp. 157-186 ◽  
Author(s):  
Frank E. Curtis ◽  
Nicholas I.M. Gould ◽  
Hao Jiang ◽  
Daniel P. Robinson
Keyword(s):  
Augmented Lagrangian ◽  
Augmented Lagrangian Methods ◽  
Numerical Experience ◽  
Lagrangian Methods
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