Structural and Multidisciplinary Optimization
, Volume 37, Issue 5, pp 435446
First online:
A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics
 José HerskovitsAffiliated withCOPPE, Mechanical Eng. Prog., Federal University of Rio de Janeiro Email author
 , Sandro R. MazorcheAffiliated withDepartment of Mathematics, UFJF, ICE Campus Universitário, Federal University of Juiz de Fora
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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 Title
 A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics
 Journal

Structural and Multidisciplinary Optimization
Volume 37, Issue 5 , pp 435446
 Cover Date
 200902
 DOI
 10.1007/s0015800802525
 Print ISSN
 1615147X
 Online ISSN
 16151488
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Feasible direction algorithm
 Interior point algorithm
 Nonlinear complementarity problems
 Variational formulations in mechanics
 Industry Sectors
 Authors

 José Herskovits ^{(1)}
 Sandro R. Mazorche ^{(2)}
 Author Affiliations

 1. COPPE, Mechanical Eng. Prog., Federal University of Rio de Janeiro, Caixa Postal 68503, 21945 970, Rio de Janeiro, Brazil
 2. Department of Mathematics, UFJF, ICE Campus Universitário, Federal University of Juiz de Fora, CEP 36036330, Juiz de ForaMG, Brazil