An Interior Point Algorithm for Mixed Complementarity Nonlinear Problems

Nonlinear complementarity and mixed complementarity problems arise in mathematical models describing several applications in Engineering, Economics and different branches of physics. Previously, robust and efficient feasible directions interior point algorithm was presented for nonlinear complementa...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2017-11, Vol.175 (2), p.432-449
Main Authors: Gutierrez, Angel E. R., Mazorche, Sandro R., Herskovits, José, Chapiro, Grigori
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Economic models
Engineering
Iterative methods
Mathematical models
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Robustness (mathematics)
Solid mechanics
Theory of Computation
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Summary:Nonlinear complementarity and mixed complementarity problems arise in mathematical models describing several applications in Engineering, Economics and different branches of physics. Previously, robust and efficient feasible directions interior point algorithm was presented for nonlinear complementarity problems. In this paper, it is extended to mixed nonlinear complementarity problems. At each iteration, the algorithm finds a feasible direction with respect to the region defined by the inequality conditions, which is also monotonic descent direction for the potential function. Then, an approximate line search along this direction is performed in order to define the next iteration. Global and asymptotic convergence for the algorithm is investigated. The proposed algorithm is tested on several benchmark problems. The results are in good agreement with the asymptotic analysis. Finally, the algorithm is applied to the elastic–plastic torsion problem encountered in the field of Solid Mechanics.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1171-7