On merit functions for p-order cone complementarity problem

2016 ◽  
Vol 67 (1) ◽  
pp. 155-173 ◽  
Author(s):  
Xin-He Miao ◽  
Yu-Lin Chang ◽  
Jein-Shan Chen
Keyword(s):  
Complementarity Problem ◽  
Merit Functions

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.

scholarly journals ON SOME NCP-FUNCTIONS BASED ON THE GENERALIZED FISCHER–BURMEISTER FUNCTION

2007 ◽  
Vol 24 (03) ◽  
pp. 401-420 ◽  
Author(s):  
JEIN-SHAN CHEN
Keyword(s):  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Unconstrained Minimization ◽  
Merit Functions ◽  
Nonlinear Complementarity

In this paper, we study several NCP-functions for the nonlinear complementarity problem (NCP) which are indeed based on the generalized Fischer–Burmeister function, ϕp(a, b) = ||(a, b)||p - (a + b). It is well known that the NCP can be reformulated as an equivalent unconstrained minimization by means of merit functions involving NCP-functions. Thus, we aim to investigate some important properties of these NCP-functions that will be used in solving and analyzing the reformulation of the NCP.

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 Merit functions for absolute value variational inequalities

2021 ◽  
Vol 6 (11) ◽  
pp. 12133-12147
Author(s):  
Safeera Batool ◽  
◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Keyword(s):  
Variational Inequalities ◽  
Error Bounds ◽  
Complementarity Problem ◽  
Merit Functions ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Special Cases ◽  
The Absolute

<abstract><p>This article deals with a class of variational inequalities known as absolute value variational inequalities. Some new merit functions for the absolute value variational inequalities are established. Using these merit functions, we derive the error bounds for absolute value variational inequalities. Since absolute value variational inequalities contain variational inequalities, absolute value complementarity problem and system of absolute value equations as special cases, the findings presented here recapture various known results in the related domains. The conclusions of this paper are more comprehensive and may provoke futuristic research.</p></abstract>

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