Globally convergent limited memory bundle method for large-scale nonsmooth optimization

2006 ◽  
Vol 109 (1) ◽  
pp. 181-205 ◽  
Author(s):  
Napsu Haarala ◽  
Kaisa Miettinen ◽  
Marko M. Mäkelä
Keyword(s):  
Nonsmooth Optimization ◽  
Large Scale ◽  
Bundle Method ◽  
Limited Memory ◽  
Globally Convergent

New limited memory bundle method for large-scale nonsmooth optimization

2004 ◽  
Vol 19 (6) ◽  
pp. 673-692 ◽  
Author(s):  
M. Haarala ◽  
K. Miettinen † ◽  
M. M. Mäkelä ‡
Keyword(s):  
Nonsmooth Optimization ◽  
Large Scale ◽  
Bundle Method ◽  
Limited Memory

scholarly journals Solving the Short-Term Scheduling Problem of Hydrothermal Systems via Lagrangian Relaxation and Augmented Lagrangian

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Rafael N. Rodrigues ◽  
Edson L. da Silva ◽  
Erlon C. Finardi ◽  
Fabricio Y. K. Takigawa
Keyword(s):  
Lagrangian Relaxation ◽  
Large Scale ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Real Life ◽  
Hydrothermal Systems ◽  
Bundle Method ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Short Term

This paper addresses the short-term scheduling problem of hydrothermal power systems, which results in a large-scale mixed-integer nonlinear programming problem. The objective consists in minimizing the operation cost over a two-day horizon with a one-hour time resolution. To solve this difficult problem, a Lagrangian Relaxation (LR) based on variable splitting is designed where the resulting dual problem is solved by a Bundle method. Given that the LR usually fails to find a feasible solution, we use an inexact Augmented Lagrangian method to improve the quality of the solution supplied by the LR. We assess our approach by using a real-life hydrothermal configuration extracted from the Brazilian power system, proving the conceptual and practical feasibility of the proposed algorithm. In summary, the main contributions of this paper are (i) a detailed and compatible modelling for this problem is presented; (ii) in order to solve efficiently the entire problem, a suitable decomposition strategy is presented. As a result of these contributions, the proposed model is able to find practical solutions with moderate computational burden, which is absolutely necessary in the modern power industry.

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