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On Generalized Positive Subdefinite Matrices and Interior Point Algorithm

  • 2018
  • OriginalPaper
  • Chapter
Published in:
Authors
A. K. Das
R. Jana
Deepmala
Published in
Operations Research and Optimization
Publisher
Springer Singapore

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Abstract

In this paper, we propose an iterative and descent type interior point method to compute solution of linear complementarity problem LCP(q, A) given that A is real square matrix and q is a real vector. The linear complementarity problem includes many of the optimization problems and applications. In this context, we consider the class of generalized positive subdefinite matrices (GPSBD) which is a generalization of the class of positive subdefinite (PSBD) matrices. Though Lemke’s algorithm is frequently used to solve small and medium-size LCP(q, A), Lemke’s algorithm does not compute solution of all problems. It is known that Lemke’s algorithm is not a polynomial time bound algorithm. We show that the proposed algorithm converges to the solution of LCP(q, A) where A belongs to GPSBD class. We provide the complexity analysis of the proposed algorithm. A numerical example is illustrated to show the performance of the proposed algorithm.

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next chapter Saddle Point Criteria for Semi-infinite Programming Problems via an -Approximation Method
Title
On Generalized Positive Subdefinite Matrices and Interior Point Algorithm
Authors
A. K. Das
R. Jana
Deepmala
Copyright Year
2018
Publisher
Springer Singapore
Book
Operations Research and Optimization

Print ISBN: 978-981-10-7813-2

Electronic ISBN: 978-981-10-7814-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-981-10-7814-9_1
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