scholarly journals Strong Convergence on the Aggregate Constraint-Shifting Homotopy Method for Solving General Nonconvex Programming

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhichuan Zhu ◽  
Yeong-Cheng Liou
Keyword(s):  
Nonlinear Programming ◽  
Strong Convergence ◽  
Nonconvex Programming ◽  
Inequality Constraint ◽  
Homotopy Method ◽  
Cone Condition ◽  
Globally Convergent ◽  
Weaker Conditions ◽  
Convergent Solution ◽  
T System

In the paper, the aggregate constraint-shifting homotopy method for solving general nonconvex nonlinear programming is considered. The aggregation is only about inequality constraint functions. Without any cone condition for the constraint functions, the existence and convergence of the globally convergent solution to the K-K-T system are obtained for both feasible and infeasible starting points under much weaker conditions.

Aggregate Constraint Homotopy Method for Nonlinear Programming on Unbounded Set

2011 ◽  
Vol 50-51 ◽  
pp. 283-287
Author(s):  
Yu Xiao ◽  
Hui Juan Xiong ◽  
Zhi Gang Yan
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Additional Assumption ◽  
Normal Cone ◽  
Constraint Qualifications ◽  
Convergence Result ◽  
Homotopy Method ◽  
Cone Condition ◽  
Feasible Set

In [1], an aggregate constraint aggregate (ACH) method for nonconvex nonlinear programming problems was presented and global convergence result was obtained when the feasible set is bounded and satisfies a weak normal cone condition with some standard constraint qualifications. In this paper, without assuming the boundedness of feasible set, the global convergence of ACH method is proven under a suitable additional assumption.

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.

The aggregate constraint homotopy method for nonconvex nonlinear programming

2001 ◽  
Vol 45 (7) ◽  
pp. 839-847 ◽  
Author(s):  
Bo Yu ◽  
Guo-chen Feng ◽  
Shao-Liang Zhang
Keyword(s):  
Nonlinear Programming ◽  
Homotopy Method

scholarly journals A globally convergent primal-dual interior-point filter method for nonlinear programming

2004 ◽  
Vol 100 (2) ◽  
pp. 379-410 ◽  
Author(s):  
Michael Ulbrich ◽  
Stefan Ulbrich ◽  
Lu�s N. Vicente
Keyword(s):  
Nonlinear Programming ◽  
Interior Point ◽  
Filter Method ◽  
Globally Convergent ◽  
Primal Dual
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