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New global error bound for extended linear complementarity problems.

Hongchun Sun1, Min Sun2,3, Yiju Wang3

  • 11School of Mathematics and Statistics, Linyi University, Linyi, China.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary
This summary is machine-generated.

Researchers developed new global error bounds for the extended linear complementarity problem (ELCP) using a novel residual function. These findings apply to vertical and mixed linear complementarity problems under weaker conditions, offering broader applicability than previous methods.

Keywords:
ELCPGlobal error boundResidual function

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Area of Science:

  • Optimization Theory
  • Numerical Analysis
  • Mathematical Programming

Background:

  • The extended linear complementarity problem (ELCP) is a significant area in mathematical programming.
  • Existing methods for error bounds in ELCP often require strong conditions.
  • There is a need for more general and robust error bound techniques for ELCP variants.

Purpose of the Study:

  • To establish a new type of global error bound for the extended linear complementarity problem (ELCP).
  • To derive global error bounds for vertical and mixed linear complementarity problems.
  • To extend the applicability of error bounds to a more general class of ELCPs.

Main Methods:

  • Introduction of a novel residual function tailored for ELCP.
  • Theoretical derivation of global error bounds based on the new residual function.
  • Analysis of error bounds under weaker conditions compared to existing literature.

Main Results:

  • A new global error bound for the extended linear complementarity problem (ELCP) is established.
  • New global error bounds are obtained for the vertical linear complementarity problem and the mixed linear complementarity problem.
  • The derived error bounds are applicable under weaker conditions, enhancing their generality.

Conclusions:

  • The proposed method provides improved and more general global error bounds for various linear complementarity problems.
  • The findings supplement and extend recent results in the field of error bounds for ELCP.
  • Numerical experiments confirm the feasibility and effectiveness of the new error bound techniques.