Abstract
Linear Complementarity Problems (LCPs) belong to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Following our recently published ideas we generalize affine scaling and predictor-corrector interior point algorithms to solve LCPs with general matrices in EP-sense, namely, our generalized interior point algorithms either solve the problems with rational coefficient matrix in polynomial time or give a polynomial size certificate that our matrix does not belong to the set of P * (~κ) matrices, with arbitrary large, but apriori fixed, rational, positive ~κ.
| Original language | English |
|---|---|
| Pages (from-to) | 1-12 |
| Number of pages | 12 |
| Journal | Algorithmic Operations Research |
| Volume | 5 |
| Issue number | 1 |
| Publication status | Published - 1 Jan 2010 |
Keywords
- linear complementarity problem
- sufficient matrix
- interior point method
- affine scaling method
- predictor-corrector algorithm