scholarly journals A Two-Parametric Class of Merit Functions for the Second-Order Cone Complementarity Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoni Chi ◽  
Zhongping Wan ◽  
Zijun Hao
Keyword(s):  
Complementarity Problem ◽  
Unconstrained Minimization ◽  
Merit Function ◽  
Second Order ◽  
Merit Functions ◽  
New Class ◽  
Second Order Cone ◽  
Bounded Level Sets ◽  
The One ◽  
Parametric Class

We propose a two-parametric class of merit functions for the second-order cone complementarity problem (SOCCP) based on the one-parametric class of complementarity functions. By the new class of merit functions, the SOCCP can be reformulated as an unconstrained minimization problem. The new class of merit functions is shown to possess some favorable properties. In particular, it provides a global error bound ifFandGhave the joint uniform CartesianP-property. And it has bounded level sets under a weaker condition than the most available conditions. Some preliminary numerical results for solving the SOCCPs show the effectiveness of the merit function method via the new class of merit functions.

scholarly journals The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoni Chi ◽  
Zhongping Wan ◽  
Zijun Hao
Keyword(s):  
Directional Derivative ◽  
Second Order ◽  
Smoothing Function ◽  
Smoothing Methods ◽  
Second Order Cone ◽  
Complementarity Functions ◽  
Computable Formula ◽  
Smoothing Functions ◽  
The One ◽  
Parametric Class

Second-order cone (SOC) complementarity functions and their smoothing functions have been much studied in the solution of second-order cone complementarity problems (SOCCP). In this paper, we study the directional derivative and B-subdifferential of the one-parametric class of SOC complementarity functions, propose its smoothing function, and derive the computable formula for the Jacobian of the smoothing function. Based on these results, we prove the Jacobian consistency of the one-parametric class of smoothing functions, which will play an important role for achieving the rapid convergence of smoothing methods. Moreover, we estimate the distance between the subgradient of the one-parametric class of the SOC complementarity functions and the gradient of its smoothing function, which will help to adjust a parameter appropriately in smoothing methods.

scholarly journals On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem

2013 ◽  
Vol 83 (287) ◽  
pp. 1143-1171 ◽  
Author(s):  
Shaohua Pan ◽  
Sangho Kum ◽  
Yongdo Lim ◽  
Jein-Shan Chen
Keyword(s):  
Complementarity Problem ◽  
Merit Function ◽  
Second Order ◽  
Second Order Cone

scholarly journals Further Application ofH-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Wei-Zhe Gu ◽  
Mohamed A. Tawhid
Keyword(s):  
Stationary Point ◽  
Complementarity Problem ◽  
Global Minimum ◽  
Complementarity Problems ◽  
Merit Function ◽  
Merit Functions ◽  
Generalized Complementarity Problem ◽  
Nonlinear Complementarity ◽  
Generalized Complementarity Problems ◽  
The Given

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) wherefandgareH-differentiable. We describeH-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on theH-differentials offandg, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g)to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved forC1, semismooth, and locally Lipschitzian.

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