A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics Authors José Herskovits COPPE, Mechanical Eng. Prog. Federal University of Rio de Janeiro Sandro R. Mazorche Department of Mathematics, UFJF, ICE Campus Universitário Federal University of Juiz de Fora Research Paper

First Online: 12 April 2008 Received: 02 August 2007 Revised: 05 February 2008 Accepted: 09 February 2008 DOI :
10.1007/s00158-008-0252-5

Cite this article as: Herskovits, J. & Mazorche, S.R. Struct Multidisc Optim (2009) 37: 435. doi:10.1007/s00158-008-0252-5
Abstract
Complementarity problems are involved in mathematical models of several applications in engineering, economy and different branches of physics. We mention contact problems and dynamics of multiple bodies systems in solid mechanics. In this paper we present a new feasible direction algorithm for nonlinear complementarity problems. This one begins at an interior point, strictly satisfying the inequality conditions, and generates a sequence of interior points that converges to a solution of the problem. At each iteration, a feasible direction is obtained and a line search performed, looking for a new interior point with a lower value of an appropriate potential function. We prove global convergence of the present algorithm and present a theoretical study about the asymptotic convergence. Results obtained with several numerical test problems, and also application in mechanics, are described and compared with other well known techniques. All the examples were solved very efficiently with the present algorithm, employing always the same set of parameters.

Keywords
Feasible direction algorithm
Interior point algorithm
Nonlinear complementarity problems
Variational formulations in mechanics

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