scholarly journals Differentiability v.s. convexity for complementarity functions

2015 ◽  
Vol 11 (1) ◽  
pp. 209-216 ◽  
Author(s):  
Chien-Hao Huang ◽  
Jein-Shan Chen ◽  
Juan Enrique Martinez-Legaz
Keyword(s):  
Complementarity Functions

scholarly journals A Double Nonmonotone Quasi-Newton Method for Nonlinear Complementarity Problem Based on Piecewise NCP Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhensheng Yu ◽  
Zilun Wang ◽  
Ke Su
Keyword(s):  
Global Convergence ◽  
Newton Method ◽  
Complementarity Problem ◽  
Line Search ◽  
Nonlinear Complementarity Problem ◽  
Practical Applications ◽  
Nonlinear Complementarity ◽  
Complementarity Functions ◽  
Single Solution ◽  
Quasi Newton

In this paper, a double nonmonotone quasi-Newton method is proposed for the nonlinear complementarity problem. By using 3-1 piecewise and 4-1 piecewise nonlinear complementarity functions, the nonlinear complementarity problem is reformulated into a smooth equation. By a double nonmonotone line search, a smooth Broyden-like algorithm is proposed, where a single solution of a smooth equation at each iteration is required with the reduction in the scale of the calculation. Under suitable conditions, the global convergence of the algorithm is proved, and numerical results with some practical applications are given to show the efficiency of the algorithm.

Penalized complementarity functions on symmetric cones

2009 ◽  
Vol 46 (3) ◽  
pp. 475-485 ◽  
Author(s):  
Sangho Kum ◽  
Yongdo Lim
Keyword(s):  
Symmetric Cones ◽  
Complementarity Functions

scholarly journals A local Jacobian smoothing method for solving Nonlinear Complementarity Problems

2020 ◽  
Vol 25 (1) ◽  
pp. 149-174
Author(s):  
Favian E Arenas ◽  
Héctor Jairo Martínez ◽  
Rosana Pérez
Keyword(s):  
Complementarity Problem ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Smoothing Method ◽  
System Of Equations ◽  
Nonlinear Complementarity ◽  
Complementarity Functions ◽  
Type Algorithm ◽  
Numerical Performance ◽  
Generalized Newton

In this paper, we present a smoothing of a family of nonlinear complementarity functions and use its properties in combination with the smooth Jacobian strategy to present a new generalized Newton-type algorithm to solve a nonsmooth system of equations equivalent to the Nonlinear Complementarity Problem. In addition, we prove that the algorithm converges locally and q-quadratically, and analyze its numerical performance.

scholarly journals Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Juhe Sun ◽  
Xiao-Ren Wu ◽  
B. Saheya ◽  
Jein-Shan Chen ◽  
Chun-Hsu Ko
Keyword(s):  
Neural Network ◽  
Second Order ◽  
Merit Functions ◽  
Second Order Cone ◽  
The Neural Network ◽  
Complementarity Functions ◽  
Type Classes ◽  
Quadratic Programming Problems ◽  
Numerical Performance ◽  
Discrete Type

This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.

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