scholarly journals Global Error Bound Estimation for the Generalized Nonlinear Complementarity Problem over a Closed Convex Cone

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hongchun Sun ◽  
Yiju Wang
Keyword(s):  
Error Bound ◽  
Complementarity Problem ◽  
Convex Cone ◽  
Nonlinear Complementarity Problem ◽  
Global Error ◽  
Closed Convex Cone ◽  
Global Error Bound ◽  
Nonlinear Complementarity ◽  
Bound Estimation

The global error bound estimation for the generalized nonlinear complementarity problem over a closed convex cone (GNCP) is considered. To obtain a global error bound for the GNCP, we first develop an equivalent reformulation of the problem. Based on this, a global error bound for the GNCP is established. The results obtained in this paper can be taken as an extension of previously known results.

scholarly journals A Sharper Global Error Bound for the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hongchun Sun ◽  
Yiju Wang
Keyword(s):  
Error Bound ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Global Error ◽  
Global Error Bound ◽  
Equivalent Formulation ◽  
Nonlinear Complementarity ◽  
Weaker Conditions ◽  
Bound Estimation

We revisit the global error bound for the generalized nonlinear complementarity problem over a polyhedral cone (GNCP). By establishing a new equivalent formulation of the GNCP, we establish a sharper global error bound for the GNCP under weaker conditions, which improves the existing error bound estimation for the problem.

scholarly journals An Improvement of Global Error Bound for the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hongchun Sun ◽  
Yiju Wang ◽  
Houchun Zhou ◽  
Shengjie Li
Keyword(s):  
Error Bound ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Global Error ◽  
New Technique ◽  
Global Error Bound ◽  
Nonlinear Complementarity ◽  
A New Technique ◽  
Weaker Conditions

We consider the global error bound for the generalized nonlinear complementarity problem over a polyhedral cone (GNCP). By a new technique, we establish an easier computed global error bound for the GNCP under weaker conditions, which improves the result obtained by Sun and Wang (2013) for GNCP.

scholarly journals A complex nonlinear complementarity problem

1978 ◽  
Vol 19 (3) ◽  
pp. 437-444 ◽  
Author(s):  
Sribatsa Nanda ◽  
Sudarsan Nanda
Keyword(s):  
Continuous Function ◽  
Complementarity Problem ◽  
Convex Cone ◽  
Existence And Uniqueness ◽  
Nonlinear Complementarity Problem ◽  
Closed Convex Cone ◽  
Uniqueness Of Solutions ◽  
Existence Of A Solution ◽  
Polar Cone ◽  
Nonlinear Complementarity

In this paper we study the existence and uniqueness of solutions for the following complex nonlinear complementarity problem: find z ∈ S such that g(z) ∈ S* and re(g(z), z) = 0, where S is a closed convex cone in Cn, S* the polar cone, and g is a continuous function from Cn into itself. We show that the existence of a z ∈ S with g(z) ∈ int S* implies the existence of a solution to the nonlinear complementarity problem if g is monotone on S and the solution is unique if g is strictly monotone. We also show that the above problem has a unique solution if the mapping g is strongly monotone on S.

A New Type Algorithm for the Extended Complementarity Problem in Engineering Modeling

2011 ◽  
Vol 320 ◽  
pp. 620-625
Author(s):  
Cheng Jiang Yin
Keyword(s):  
Global Convergence ◽  
Error Bound ◽  
Complementarity Problem ◽  
Global Error ◽  
Global Error Bound ◽  
Type Algorithm ◽  
New Type ◽  
Engineering Modeling ◽  
Bound Estimation

In this paper, we consider extended complementarity problem(ECP) in engineering modeling. To solve the problem, first, under the suitable conditions, we present an easily computable global error bound for the ECP, and then propose a new type algorithm to solve the ECP based on the error bound estimation. The global convergence is also established.

SOME PROPERTIES OF A CLASS OF MERIT FUNCTIONS FOR SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

2006 ◽  
Vol 23 (04) ◽  
pp. 473-495 ◽  
Author(s):  
YONG-JIN LIU ◽  
LI-WEI ZHANG ◽  
YIN-HE WANG
Keyword(s):  
Error Bound ◽  
Complementarity Problems ◽  
Symmetric Cone ◽  
Merit Function ◽  
Nonlinear Complementarity Problems ◽  
Global Error ◽  
Merit Functions ◽  
Global Error Bound ◽  
Nonlinear Complementarity

In this paper, we extend a class of merit functions proposed by Kanzow et al. (1997) for linear/nonlinear complementarity problems to Symmetric Cone Complementarity Problems (SCCP). We show that these functions have several interesting properties, and establish a global error bound for the solution to the SCCP as well as the level boundedness of every merit function under some mild assumptions. Moreover, several functions are demonstrated to enjoy these properties.

scholarly journals A nonlinear complementarity problem in mathematical programming in Hilbert space

1979 ◽  
Vol 20 (2) ◽  
pp. 233-236 ◽  
Author(s):  
Sribatsa Nanda ◽  
Sudarsan Nanda
Keyword(s):  
Hilbert Space ◽  
Complementarity Problem ◽  
Existence And Uniqueness ◽  
Nonlinear Complementarity Problem ◽  
Closed Convex Cone ◽  
Existence And Uniqueness Theorem ◽  
Polar Cone ◽  
Nonlinear Complementarity ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper we prove the following existence and uniqueness theorem for the nonlinear complementarity problem by using the Banach contraction principle. If T: K → H is strongly monotone and lipschitzian with k2 < 2c < k2+1, then there is a unique y ∈ K, such that Ty ∈ K* and (Ty, y) = 0 where H is a Hilbert space, K is a closed convex cone in H, and K* the polar cone.

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