ISSN:
1436-4646

Keywords:
Linear complementarity problem
;
polynomial-time algorithm
;
path of centers
;
Karmarkar's algorithm

Source:
Springer Online Journal Archives 1860-2000

Topics:
Computer Science
,
Mathematics

Notes:
Abstract Given ann × n matrixM and ann-dimensional vectorq, the problem of findingn-dimensional vectorsx andy satisfyingy = Mx + q, x ≥ 0,y ≥ 0,x i y i = 0 (i = 1, 2,⋯,n) is known as a linear complementarity problem. Under the assumption thatM is positive semidefinite, this paper presents an algorithm that solves the problem in O(n 3 L) arithmetic operations by tracing the path of centers,{(x, y) ∈ S: x i y i =μ (i = 1, 2,⋯,n) for some μ 〉 0} of the feasible regionS = {(x, y) ≥ 0:y = Mx + q}, whereL denotes the size of the input data of the problem.

Type of Medium:
Electronic Resource

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