Gap Functions and Algorithms for Variational Inequality Problems | Zendy

Congjun Zhang | Zendy; Baoqing Liu | Zendy; Jun S. Wei | Zendy

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Gap Functions and Algorithms for Variational Inequality Problems

Author(s) -

Congjun Zhang,

Baoqing Liu,

Jun S. Wei

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/965640

Subject(s) - variational inequality , mathematics , convergence (economics) , constraint (computer aided design) , method of steepest descent , function (biology) , gradient descent , set (abstract data type) , variational analysis , inequality , mathematical optimization , computer science , mathematical analysis , artificial neural network , geometry , evolutionary biology , machine learning , economics , biology , programming language , economic growth

We solve several kinds of variational inequality problems through gap functions, give algorithms for the corresponding problems, obtain global error bounds, and make the convergence analysis. By generalized gap functions and generalized D-gap functions, we give global bounds for the set-valued mixed variational inequality problems. And through gap function, we equivalently transform the generalized variational inequality problem into a constraint optimization problem, give the steepest descent method, and show the convergence of the method. © 2013 Congjun Zhang et al.

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