Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems | Zendy

Goran Lešaja | Zendy

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Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems

Author(s) -

Goran Lešaja

Publication year - 2002

Publication title -

yugoslav journal of operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.221

H-Index - 21

eISSN - 1820-743X

pISSN - 0354-0243

DOI - 10.2298/yjor0201017l

Subject(s) - mathematics , invertible matrix , lipschitz continuity , linear complementarity problem , complementarity theory , mixed complementarity problem , nonlinear complementarity problem , complementarity (molecular biology) , homogeneous , quadratic equation , jacobian matrix and determinant , interior point method , algorithm , convergence (economics) , nonlinear system , mathematical optimization , solution set , set (abstract data type) , mathematical analysis , computer science , combinatorics , pure mathematics , geometry , physics , quantum mechanics , biology , economics , genetics , programming language , economic growth

A P*-Nonlinear Complementarity Problem as a generalization of the P*-Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set

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