Theorems on the global convergence of the nonlinear homotopy method for MOS circuits

2011 ◽  
Author(s):  
Dan Niu ◽  
Guangming Hu ◽  
Yasuaki Inoue
Keyword(s):  
Global Convergence ◽  
Homotopy Method ◽  
Mos Circuits

Smoothing Homotopy Method for Solving Second-Order Cone Complementarity Problem

2020 ◽  
Vol 37 (05) ◽  
pp. 2050023
Author(s):  
Xiaona Fan ◽  
Min Zeng ◽  
Li Jiang
Keyword(s):  
Global Convergence ◽  
Smooth Function ◽  
Complementarity Problem ◽  
Homotopy Method ◽  
Second Order ◽  
Numerical Results ◽  
Monotonicity Condition ◽  
Second Order Cone

In this paper, based on Chen–Harker–Kanzow–Smale smooth function, we obtain a smoothing homotopy method to solve the second-order cone complementarity problem. The global convergence is ensured under certain non-monotonicity condition for the defined mapping [Formula: see text]. The numerical results illustrate that this method is feasible.

A New Proof for Global Convergence of a Smoothing Homotopy Method for the Nonlinear Complementarity Problem

2018 ◽  
Vol 35 (04) ◽  
pp. 1850027
Author(s):  
Xiaona Fan ◽  
Qinglun Yan
Keyword(s):  
Global Convergence ◽  
Complementarity Problem ◽  
Interior Point Method ◽  
Nonlinear Complementarity Problem ◽  
Initial Point ◽  
Smooth Curve ◽  
Homotopy Method ◽  
Nonlinear Complementarity ◽  
Solution Condition ◽  
Almost All

In this paper, we propose a new proof for smoothing homotopy method based on the Fischer–Burmeister function to solve the nonlinear complementarity problem under a nonmonotone solution condition. Under this assumption condition imposed on the defined mapping [Formula: see text], global convergence of a smooth curve determined by the referred homotopy equation is established for almost all initial points in [Formula: see text] and it is actually regarded as an interior point method. Besides, if the initial point is expanded to [Formula: see text], the global convergence of the homotopy method is ensured under a similar condition. The numerical results are reported and illustrate that the method is efficient for some nonlinear complementarity problems.

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.

A class of homotopy with regularization for nonlinear ill-posed problems in Hilbert space

2019 ◽  
Vol 27 (4) ◽  
pp. 487-499
Author(s):  
Minghui Liu ◽  
Fuming Ma
Keyword(s):  
Hilbert Space ◽  
Inverse Problems ◽  
Global Convergence ◽  
Newton Method ◽  
Tikhonov Regularization ◽  
Homotopy Method ◽  
Numerical Schemes ◽  
Numerical Examples ◽  
Ill Posed ◽  
Regularized Newton Method

Abstract Nonlinear ill-posed problems arise in many inverse problems in Hilbert space. We investigate the homotopy method, which can obtain global convergence to solve the problems. The “homotopy with Tikhonov regularization” and “homotopy without derivative” are developed in this paper. The existence of the homotopy curve is proved. Several numerical schemes for tracing the homotopy curve are given, including adaptive tracing skills. Compared to the regularized Newton method, the numerical examples show that our proposed methods are stable and effective.

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