MCPLIB: A Collection of Nonlinear Mixed Complementarity Problems. The origins and some motivational details of a collection of nonlinear mixed complementarity problems are given. This collection serves two purposes. Firstly, it gives a uniform basis for testing currently available and new algorithms for mixed complementarity problems. Function and Jacobian evaluations for the resulting problems are provided via a GAMS interface, making thorough testing of algorithms on practical complementarity problems possible. Secondly, it gives examples of how to formulate many popular problem formats as mixed complementarity problems and how to describe the resulting problems in GAMS format. We demonstrate the ease and power of formulating practical models in the MCP format. Given these examples, it is hoped that this collection will grow to include many problems that test complementarity algorithms more fully. The collection is available by anonymous ftp. Computational results using the PATH solver covering all of these problems are described

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  1. Fan, Bin; Ma, Changfeng; Wu, Aidi; Wu, Chao: A Levenberg-Marquardt method for nonlinear complementarity problems based on nonmonotone trust region and line search techniques (2018)
  2. Gao, Peiting; He, Chuanjiang: An efficient three-term conjugate gradient method for nonlinear monotone equations with convex constraints (2018)
  3. Ou, Yigui; Li, Jingya: A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints (2018)
  4. Tawhid, Mohamed A.; Gu, Wei-Zhe; Tran, Benjamin: A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions (2018)
  5. Zhao, Na; Ni, Tie: A nonmonotone smoothing Newton algorithm for solving general box constrained variational inequalities (2018)
  6. Bolzon, Gabriella: Complementarity problems in structural engineering: an overview (2017)
  7. Fan, Bin: A nonmonotone Levenberg-Marquardt method for nonlinear complementarity problems under local error bound (2017)
  8. Feng, Dexiang; Sun, Min; Wang, Xueyong: A family of conjugate gradient methods for large-scale nonlinear equations (2017)
  9. Gutierrez, Angel E. R.; Mazorche, Sandro R.; Herskovits, José; Chapiro, Grigori: An interior point algorithm for mixed complementarity nonlinear problems (2017)
  10. Hart, William E.; Laird, Carl D.; Watson, Jean-Paul; Woodruff, David L.; Hackebeil, Gabriel A.; Nicholson, Bethany L.; Siirola, John D.: Pyomo -- optimization modeling in Python (2017)
  11. Lamm, Michael; Lu, Shu; Budhiraja, Amarjit: Individual confidence intervals for solutions to expected value formulations of stochastic variational inequalities (2017)
  12. Liu, Jinkui; Li, Shengjie: Multivariate spectral DY-type projection method for convex constrained nonlinear monotone equations (2017)
  13. Liu, J. K.; Li, S. J.: A three-term derivative-free projection method for nonlinear monotone system of equations (2016)
  14. Sun, Min; Liu, Jing: New hybrid conjugate gradient projection method for the convex constrained equations (2016)
  15. Tian, Boshi; Li, Donghui; Yang, Xiaoqi: An unconstrained differentiable penalty method for implicit complementarity problems (2016)
  16. Tian, Boshi; Yang, Xiaoqi: Smoothing power penalty method for nonlinear complementarity problems (2016)
  17. Fan, Bin: A smoothing Broyden-like method with a nonmonotone derivative-free line search for nonlinear complementarity problems (2015)
  18. Liu, Jing; Duan, Yongrui: Two spectral gradient projection methods for constrained equations and their linear convergence rate (2015)
  19. Sun, Min; Liu, Jing: Three derivative-free projection methods for nonlinear equations with convex constraints (2015)
  20. Sun, Min; Liu, Jing: A modified Hestenes-Stiefel projection method for constrained nonlinear equations and its linear convergence rate (2015)

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