A Deflected Subgradient Method Using a General Augmented Lagrangian Duality with Implications on Penalty Methods

2010 ◽  
pp. 109-132 ◽  
Author(s):  
Regina S. Burachik ◽  
C. Yalçın Kaya
Keyword(s):  
Augmented Lagrangian ◽  
Subgradient Method ◽  
Lagrangian Duality ◽  
Penalty Methods

scholarly journals Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. Application to hydroplaning flows interacting with real tire tread patterns

2011 ◽  
Vol 230 (4) ◽  
pp. 956-983 ◽  
Author(s):  
Stéphane Vincent ◽  
Arthur Sarthou ◽  
Jean-Paul Caltagirone ◽  
Fabien Sonilhac ◽  
Pierre Février ◽  
...  
Keyword(s):  
Augmented Lagrangian ◽  
Penalty Methods ◽  
Two Phase Flows ◽  
Two Phase

Further Study on Augmented Lagrangian Duality Theory

2005 ◽  
Vol 31 (2) ◽  
pp. 193-210 ◽  
Author(s):  
X. X. Huang ◽  
X. Q. Yang
Keyword(s):  
Duality Theory ◽  
Augmented Lagrangian ◽  
Lagrangian Duality

Exact augmented Lagrangian duality for mixed integer linear programming

2016 ◽  
Vol 161 (1-2) ◽  
pp. 365-387 ◽  
Author(s):  
Mohammad Javad Feizollahi ◽  
Shabbir Ahmed ◽  
Andy Sun
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Augmented Lagrangian ◽  
Lagrangian Duality ◽  
Mixed Integer

scholarly journals On primal convergence for augmented Lagrangian duality

Optimization ◽  
2011 ◽  
Vol 60 (8-9) ◽  
pp. 979-990 ◽  
Author(s):  
Regina S. Burachik
Keyword(s):  
Augmented Lagrangian ◽  
Lagrangian Duality

scholarly journals A Hybrid Epigraph Directions Method for Nonsmooth and Nonconvex Constrained Optimization via Generalized Augmented Lagrangian Duality and a Genetic Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-21
Author(s):  
Wilhelm P. Freire ◽  
Afonso C. C. Lemonge ◽  
Tales L. Fonseca ◽  
Hernando J. R. Franco
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Augmented Lagrangian ◽  
Dual Problem ◽  
Optimization Problems ◽  
Lagrangian Duality ◽  
Dual Function ◽  
Constrained Optimization Problems ◽  
Nonconvex Constrained Optimization ◽  
Nonsmooth And Nonconvex Optimization

The Interior Epigraph Directions (IED) method for solving constrained nonsmooth and nonconvex optimization problem via Generalized Augmented Lagrangian Duality considers the dual problem induced by a Generalized Augmented Lagrangian Duality scheme and obtains the primal solution by generating a sequence of iterates in the interior of the epigraph of the dual function. In this approach, the value of the dual function at some point in the dual space is given by minimizing the Lagrangian. The first version of the IED method uses the Matlab routine fminsearch for this minimization. The second version uses NFDNA, a tailored algorithm for unconstrained, nonsmooth and nonconvex problems. However, the results obtained with fminsearch and NFDNA were not satisfactory. The current version of the IED method, presented in this work, employs a Genetic Algorithm, which is free of any strategy to handle the constraints, a difficult task when a metaheuristic, such as GA, is applied alone to solve constrained optimization problems. Two sets of constrained optimization problems from mathematics and mechanical engineering were solved and compared with literature. It is shown that the proposed hybrid algorithm is able to solve problems where fminsearch and NFDNA fail.

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