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Feasibility problems with complementarity constraints

Author

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  • Andreani, R.
  • Júdice, J.J.
  • Martínez, J.M.
  • Martini, T.

Abstract

A Projected-Gradient Underdetermined Newton-like algorithm will be introduced for finding a solution of a Horizontal Nonlinear Complementarity Problem (HNCP) corresponding to a feasible solution of a Mathematical Programming Problem with Complementarity Constraints (MPCC). The algorithm employs a combination of Interior-Point Newton-like and Projected-Gradient directions with a line-search procedure that guarantees global convergence to a solution of HNCP or, at least, a stationary point of the natural merit function associated to this problem. Fast local convergence will be established under reasonable assumptions. The new algorithm can be applied to the computation of a feasible solution of MPCC with a target objective function value. Computational experience on test problems from well-known sources will illustrate the efficiency of the algorithm to find feasible solutions of MPCC in practice.

Suggested Citation

  • Andreani, R. & Júdice, J.J. & Martínez, J.M. & Martini, T., 2016. "Feasibility problems with complementarity constraints," European Journal of Operational Research, Elsevier, vol. 249(1), pages 41-54.
    • Handle: RePEc:eee:ejores:v:249:y:2016:i:1:p:41-54
    DOI: 10.1016/j.ejor.2015.09.030
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