The largest step path following algorithm for monotone linear complementarity problems

1997 ◽  
Vol 76 (2) ◽  
pp. 309-332 ◽  
Author(s):  
Clovis C. Gonzaga
Keyword(s):  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Path Following ◽  
Linear Complementarity ◽  
Path Following Algorithm

Path-following interior-point algorithm for monotone linear complementarity problems

2021 ◽  
Author(s):  
Welid Grimes
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Path Following ◽  
Linear Complementarity ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Barrier Parameter ◽  
Step Algorithm ◽  
Full Newton Step

This paper presents a path-following full-Newton step interior-point algorithm for solving monotone linear complementarity problems. Under new choices of the defaults of the updating barrier parameter [Formula: see text] and the threshold [Formula: see text] which defines the size of the neighborhood of the central-path, we show that the short-step algorithm has the best-known polynomial complexity, namely, [Formula: see text]. Finally, some numerical results are reported to show the efficiency of our algorithm.

Plynomial Convergence of Primal-Dual Algorithms for SDLCP Based on the Monteiro-Zhang Family of Directions

2012 ◽  
Vol 532-533 ◽  
pp. 1857-1860
Author(s):  
Guang Zhou Li
Keyword(s):  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Path Following ◽  
Complexity Bounds ◽  
New Class ◽  
Primal Dual ◽  
Carry Over ◽  
Path Following Methods ◽  
Finite Linear ◽  
Path Following Algorithm

The paper establishes the polynomial converge-nce of a new class of path-following methods for semide- finite linear complementarity problems (SDLCP) whos-se search directions belong to the class of directions introduced by Monteiro [7]. Namely, we show that the polynomial iteration complexity bounds of the well known algori-thm for linear programming, namely the short-step path-following algorithm of Kojima et al. and Monteiro and Alder, carry over to the context of SDLCP

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