Solution of a General Linear Complementarity Problem Using Smooth Optimization and Its Application to Bilinear Programming and LCP

2001 ◽  
Vol 43 (1) ◽  
pp. 1-19 ◽  
Author(s):  
L. Fernandes
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Bilinear Programming ◽  
General Linear ◽  
Smooth Optimization

SOLVING STRONGLY MONOTONE LINEAR COMPLEMENTARITY PROBLEMS

2013 ◽  
Vol 15 (04) ◽  
pp. 1340035 ◽  
Author(s):  
A. CHANDRASHEKARAN ◽  
T. PARTHASARATHY ◽  
V. VETRIVEL
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Inner Product ◽  
General Linear ◽  
Strongly Monotone ◽  
Semidefinite Linear Complementarity Problems ◽  
Lipschitz Constants

Given a linear transformation L on a finite dimensional real inner product space V to itself and an element q ∈ V we consider the general linear complementarity problem LCP (L, K, q) on a proper cone K ⊆ V. We observe that the iterates generated by any closed algorithmic map will converge to a solution for LCP (L, K, q), whenever L is strongly monotone. Lipschitz constants of L is vital in establishing the above said convergence. Hence we compute the Lipschitz constants for certain classes of Lyapunov, Stein and double-sided multiplicative transformations in the setting of semidefinite linear complementarity problems. We give a numerical illustration of a closed algorithmic map in the setting of a standard linear complementarity problem. On account of the difficulties in numerically implementing such algorithms for general linear complementarity problems, we give an alternative algorithm for computing the solution for a special class of strongly monotone semidefinite linear complementarity problems along with a numerical example.

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