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On a Homogeneous Algorithm for the Monotone Complementarity Problem
 Mathematical Programming
, 1995
"... We present a generalization of a homogeneous selfdual linear programming (LP) algorithm to solving the monotone complementarity problem (MCP). The algorithm does not need to use any "bigM" parameter or twophase method, and it generates either a solution converging towards feasibility and compleme ..."
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Cited by 26 (3 self)
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We present a generalization of a homogeneous selfdual linear programming (LP) algorithm to solving the monotone complementarity problem (MCP). The algorithm does not need to use any "bigM" parameter or twophase method, and it generates either a solution converging towards feasibility and complementarity simultaneously or a certificate proving infeasibility. Moreover, if the MCP is polynomially solvable with an interior feasible starting point, then it can be polynomially solved without using or knowing such information at all. To our knowledge, this is the first interiorpoint and infeasiblestarting algorithm for solving the MCP that possesses these desired features. Preliminary computational results are presented. Key words: Monotone complementarity problem, homogeneous and selfdual, infeasiblestarting algorithm. Running head: A homogeneous algorithm for MCP. Department of Management, Odense University, Campusvej 55, DK5230 Odense M, Denmark, email: eda@busieco.ou.dk. y De...
A Global and Local Superlinear ContinuationSmoothing Method for ... and Monotone NCP
 SIAM J. Optim
, 1997
"... We propose a continuation method for a class of nonlinear complementarity problems(NCPs), including the NCP with a P 0 and R 0 function and the monotone NCP with a feasible interior point. The continuation method is based on a class of ChenMangasarian smooth functions. Unlike many existing continua ..."
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Cited by 24 (6 self)
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We propose a continuation method for a class of nonlinear complementarity problems(NCPs), including the NCP with a P 0 and R 0 function and the monotone NCP with a feasible interior point. The continuation method is based on a class of ChenMangasarian smooth functions. Unlike many existing continuation methods, the method follows the noninterior smoothing paths, and as a result, an initial point can be easily constructed. In addition, we introduce a procedure to dynamically update the neighborhoods associated with the smoothing paths, so that the algorithm is both globally convergent and locally superlinearly convergent under suitable assumptions. Finally, a hybrid continuationsmoothing method is proposed and is shown to have the same convergence properties under weaker conditions. 1 Introduction Let F : R n ! R n be a continuously differentiable function. The nonlinear complementarity problem, denoted by NCP(F ), is to find a vector (x; y) 2 R n \Theta R n such that F (x)...
On Smoothing Methods for the P 0 Matrix Linear Complementarity Problem
, 1998
"... In this paper, we propose a BigM smoothing method for solving the P 0 matrix linear complementarity problem. We study the trajectory defined by the augmented smoothing equations and global convergence of the method under an assumption that the original P 0 matrix linear complementarity problem has ..."
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Cited by 4 (1 self)
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In this paper, we propose a BigM smoothing method for solving the P 0 matrix linear complementarity problem. We study the trajectory defined by the augmented smoothing equations and global convergence of the method under an assumption that the original P 0 matrix linear complementarity problem has a solution. Key words. linear complementarity problem, P 0 matrix, smoothing algorithm. AMS subject classifications. 65H10, 90C30, 90C33. This author's work was supported by the Australian Research Council. y This author is supported in part by NSF Grants DMI9522507 and DMS9703490. 2 1 Introduction In this paper we consider the linear complementarity problem (LCP) t T s = 0; s = Mt + q; and t; s 0; where M is an n \Theta n P 0 matrix and q is an n dimensional vector. A matrix M 2 R n\Thetan is called a P 0 matrix if max i:t i 6=0 t i (Mt) i 0; for all t 2 R n ; t 6= 0: A linear complementarity problem is called a P 0 matrix LCP if the matrix M is a P 0 matrix. The clas...
unknown title
, 2005
"... www.elsevier.com/locate/sysconle On the equivalence between complementarity systems, projected systems and differential inclusions � ..."
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www.elsevier.com/locate/sysconle On the equivalence between complementarity systems, projected systems and differential inclusions �
The Globally Uniquely Solvable Property of SecondOrder Cone Linear Complementarity Problems
, 2010
"... Abstract. The globally uniquely solvable (GUS) property of the linear transformation of the linear complementarity problems over symmetric cones has been studied recently by Gowda et al. via the approach of Euclidean Jordan algebra. In this paper, we contribute a new approach to characterizing the G ..."
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Abstract. The globally uniquely solvable (GUS) property of the linear transformation of the linear complementarity problems over symmetric cones has been studied recently by Gowda et al. via the approach of Euclidean Jordan algebra. In this paper, we contribute a new approach to characterizing the GUS property of the linear transformation of the secondorder cone linear complementarity problems (SOCLCP) via some basic linear algebra properties of the involved matrix of SOCLCP. Some more concrete and checkable sufficient and necessary conditions for the GUS property are thus derived. Key words. Secondorder cone; Linear complementarity problem; Globally uniquely solvable property AMS subject classifications. 90C33, 65K05 1