Book ChapterDOI
Finiteness of Criss-Cross Method in Complementarity Problem
A. K. Das,R. Jana,Deepmala +2 more
- Iss: 9789811046414, pp 170-180
TLDR
The criss-cross method is able to compute solution of a linear complementarity problem in finite steps in case of some new matrix classes and a numerical illustration is presented to show a comparison between criss -cross method and Lemke's algorithm with respect to number of iterations before finding a solution.Abstract:
In this paper we consider criss-cross method for finding solution of a linear complementarity problem. The criss-cross method is a pivoting procedure. We show that the criss-cross method is able to compute solution of a linear complementarity problem in finite steps in case of some new matrix classes. We present a numerical illustration to show a comparison between criss-cross method and Lemke’s algorithm with respect to number of iterations before finding a solution. Finally we raise an open problem in the context of criss-cross method.read more
Citations
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Journal ArticleDOI
On hidden Z-matrix and interior point algorithm
R. Jana,A. K. Das,A. Dutta +2 more
TL;DR: The proposed algorithm can process LCP (q, A) in polynomial time under some assumptions and is observed to be able to process the solution aspects of linear complementarity problem with hidden Z-matrix.
Journal ArticleDOI
More on hidden Z-matrices and linear complementarity problem
TL;DR: It is shown that for a non-degenerate feasible basis, linear complementarity problem with hidden Z-matrix has unique non- Degenerate solution under some assumptions.
Journal ArticleDOI
Iterative Descent Method for Generalized Leontief Model
TL;DR: In this article, the generalized Leontief model is solvable by iterative descent method based on infeasible interior point algorithm, and the convergence of the method from strictly positive starting point is proved.
Journal ArticleDOI
More on matrix splitting modulus-based iterative methods for solving linear complementarity problem
Journal ArticleDOI
On general fixed point method based on matrix splitting for solving linear complementarity problem
TL;DR: In this paper , a modified fixed point method was proposed to process the large and sparse linear complementarity problem (LCP) and formulated an equivalent fixed point equation for the LCP and showed the equivalence.
References
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Book
The Linear Complementarity Problem
TL;DR: In this article, the authors present an overview of existing and multiplicity of degree theory and propose pivoting methods and iterative methods for degree analysis, including sensitivity and stability analysis.
Journal ArticleDOI
New Finite Pivoting Rules for the Simplex Method
TL;DR: A simple proof of finiteness is given for the simplex method under an easily described pivoting rule and a second new finite version of thesimplex method is presented.
Journal ArticleDOI
The Criss-Cross Method for Solving Linear Programming Problems
TL;DR: The Criss-Cross Method of solving linear programming problems, a primal-dual scheme, normally begins with a problem solution that is neither primal nor dual feasible, and generates an optimal feasible solution in a finite number of iterations.
Journal ArticleDOI
Subdefinite Matrices and Quadratic Forms
TL;DR: In this paper, the authors define a new class of real symmetric matrices, which they call subdefinite, and investigate the properties of these matrices from a practical point of view.