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.

A New SQP Algorithm for Large-Scale Nonlinear Programming

2001 ◽  
Vol 11 (3) ◽  
pp. 716-747 ◽  
Author(s):  
R. W. H. Sargent ◽  
M. Ding
Keyword(s):  
Nonlinear Programming ◽  
Large Scale ◽  
Sqp Algorithm

scholarly journals A Proposed Extended Version of the Hadi-Vencheh Model to Improve Multiple-Criteria ABC Inventory Classification

2020 ◽  
Vol 10 (22) ◽  
pp. 8233
Author(s):  
Pei-Chun Lin ◽  
Hung-Chieh Chang
Keyword(s):  
Nonlinear Programming ◽  
Large Scale ◽  
Classification Problem ◽  
Multiple Criteria ◽  
Extended Version ◽  
Ranking Problem ◽  
Abc Classification ◽  
Proposed Model ◽  
Common Set Of Weights ◽  
Solution Efficiency

The ABC classification problem is approached as a ranking problem by the most current classification models; that is, a group of inventory items is expressed according to its overall weighted score of criteria in descending order. In this paper, we present an extended version of the Hadi-Vencheh model for multiple-criteria ABC inventory classification. The proposed model is one based on the nonlinear weighted product method (WPM), which determines a common set of weights for all items. Our proposed nonlinear WPM incorporates multiple criteria with different measured units without converting the performance of each inventory item, in terms of converting each criterion into a normalized attribute value, thereby providing an improvement over the model proposed by Hadi-Vencheh. Our study mainly includes various criteria for ABC classification and demonstrates an efficient algorithm for solving nonlinear programming problems, in which the feasible solution set does not have to be convex. The algorithm presented in this study substantially improves the solution efficiency of the canonical coordinates method (CCM) algorithm when applied to large-scale, nonlinear programming problems. The modified algorithm was tested to compare our proposed model results to the results derived using the Hadi-Vencheh model and demonstrate the algorithm’s efficacy. The practical objectives of the study were to develop an efficient nonlinear optimization solver by optimizing the quality of existing solutions, thus improving time and space efficiency.

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