# New criss-cross type algorithms for linear complementarity problems with sufficient matrices

@article{Csizmadia2006NewCT, title={New criss-cross type algorithms for linear complementarity problems with sufficient matrices}, author={Zsolt Csizmadia and Tibor Ill{\'e}s}, journal={Optimization Methods and Software}, year={2006}, volume={21}, pages={247 - 266} }

We generalize new criss-cross type algorithms for linear complementarity problems (LCPs) given with sufficient matrices. Most LCP solvers require a priori information about the input matrix. The sufficiency of a matrix is hard to be checked (no polynomial time method is known). Our algorithm is similar to Zhang's linear programming and Akkeles¸, Balogh and Illés's criss-cross type algorithm for LCP-QP problems. We modify our basic algorithm in such a way that it can start with any matrix M…

## 30 Citations

### The s-monotone index selection rule for criss-cross algorithms of linear complementarity problems

- Computer Science
- 2013

The s-monotone index selection rules for the well-known criss-cross method for solving the linear complementarity problem (LCP) are introduced and computational results obtained using the extended version of the crisscross algorithm for bi-matrix games and for the Arrow-Debreu market equilibrium problem with different market size are presented.

### Operations Research Report 2013-01 The s-Monotone Index Selection Rule for Criss-Cross Algorithms of Linear Complementarity Problems

- Computer Science
- 2013

The s-monotone index selection rules for the well-known criss-cross method for solving the linear complementarity problem (LCP) are introduced and Computational results obtained using the extended version of the crisscross algorithm for bi-matrix games and for the Arrow-Debreu market equilibrium problem with different market size are presented.

### General linear complementarity problems: algorithms and models

- Computer Science, Mathematics
- 2014

Goal of this talk is to introduce algorithms that may solve general LCPs and to show their computational performance on the well-known exchange market model of Arrow and Debreu.

### Polynomial interior point algorithms for general LCPs

- Computer Science, Mathematics
- 2007

The aim is to construct some interior point algorithms which, according to the duality theorem in EP form, gives a solution of the original problem or detects the lack of property P⁄(~•) and gives a polynomial size certiflcate of it inPolynomial time.

### Polynomial Interior Point Algorithms for General Linear Complementarity Problems

- Mathematics, Computer ScienceAlgorithmic Oper. Res.
- 2010

This work generalizes affine scaling and predictor-corrector interior point algorithms to solve LCPs with general matrices in EP-sense and suggests that either the problems with rational coefficient matrix in polynomial time or the matrix does not belong to the set of P * (~κ) matrices.

### A recursive semi-smooth Newton method for linear complementarity problems∗

- Mathematics, Computer Science
- 2016

A primal feasible active set method is presented for finding the unique solution of a Linear Complementarity Problem (LCP) with a P -matrix, which extends the globally convergent active set method…

### Interior-point algorithm for sufficient LCPs based on the technique of algebraically equivalent transformation

- Mathematics, Computer ScienceOptim. Lett.
- 2021

We present a short-step interior-point algorithm (IPA) for sufficient linear complementarity problems (LCPs) based on a new search direction. An algebraic equivalent transformation (AET) is used on…

### Predictor-corrector interior-point algorithm for sufficient linear complementarity problems based on a new type of algebraic equivalent transformation technique

- Computer Science, Mathematics
- 2020

It is proved that the new predictor-corrector (PC) interior-point algorithm (IPA) for solving linear complementarity problem (LCP) with P∗(κ)-matrices has O (1 + 4κ) √ n log 3nμ 0 4 ) iteration complexity, where κ is an upper bound of the handicap of the input matrix.

### Operations Research Report 2007-02 An EP theorem for dual linear complementarity problem

- Mathematics
- 2007

The linear complementarity problem (LCP ) belongs to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCP s without requiring some special property…

### EP Theorem for Dual Linear Complementarity Problems

- Mathematics
- 2009

AbstractThe linear complementarity problem (LCP) belongs to the class of
$\mathbb{NP}$
-hard problems. Therefore, we cannot expect a polynomial time solution method for LCPs without requiring some…

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