Large-Scale Nonlinear Programming: Decomposition Methods

1997 ◽  
pp. 259-270
Author(s):  
Kiyotaka Shimizu ◽  
Yo Ishizuka ◽  
Jonathan F. Bard
Keyword(s):  
Nonlinear Programming ◽  
Large Scale ◽  
Decomposition Methods

Large scale nonlinear programming

1983 ◽  
Vol 7 (5) ◽  
pp. 595-604 ◽  
Author(s):  
Leon S. Lasdon ◽  
A.D. Waren
Keyword(s):  
Nonlinear Programming ◽  
Large Scale

scholarly journals The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Zhengyong Zhou ◽  
Bo Yu
Keyword(s):  
Nonlinear Programming ◽  
Interior Point Method ◽  
Large Scale ◽  
State Of The Art ◽  
Numerical Procedure ◽  
Homotopy Method ◽  
Nonlinear Constraints ◽  
Computational Results ◽  
Homotopy Methods ◽  
Constraint Function

The aggregate constraint homotopy method uses a single smoothing constraint instead ofm-constraints to reduce the dimension of its homotopy map, and hence it is expected to be more efficient than the combined homotopy interior point method when the number of constraints is very large. However, the gradient and Hessian of the aggregate constraint function are complicated combinations of gradients and Hessians of all constraint functions, and hence they are expensive to calculate when the number of constraint functions is very large. In order to improve the performance of the aggregate constraint homotopy method for solving nonlinear programming problems, with few variables and many nonlinear constraints, a flattened aggregate constraint homotopy method, that can save much computation of gradients and Hessians of constraint functions, is presented. Under some similar conditions for other homotopy methods, existence and convergence of a smooth homotopy path are proven. A numerical procedure is given to implement the proposed homotopy method, preliminary computational results show its performance, and it is also competitive with the state-of-the-art solver KNITRO for solving large-scale nonlinear optimization.

scholarly journals Decomposition Methods for Large Scale LP Decoding

2013 ◽  
Vol 59 (12) ◽  
pp. 7870-7886 ◽  
Author(s):  
Siddharth Barman ◽  
Xishuo Liu ◽  
Stark C. Draper ◽  
Benjamin Recht
Keyword(s):  
Large Scale ◽  
Decomposition Methods
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