OPECgen

OPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints. We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/$^sim$danny/qpecgendoc.html.


References in zbMATH (referenced in 18 articles , 1 standard article )

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  1. Thai, Jér^ome; Bayen, Alexandre M.: Imputing a variational inequality function or a convex objective function: a robust approach (2018)
  2. Pang, Jong-Shi; Razaviyayn, Meisam; Alvarado, Alberth: Computing B-stationary points of nonsmooth DC programs (2017)
  3. Bai, Lijie; Mitchell, John E.; Pang, Jong-Shi: On conic QPCCs, conic QCQPs and completely positive programs (2016)
  4. Pang, Jong-Shi; Su, Che-Lin; Lee, Yu-Ching: A constructive approach to estimating pure characteristics demand models with pricing (2015)
  5. Wu, Jia; Zhang, Liwei; Zhang, Yi: An inexact Newton method for stationary points of mathematical programs constrained by parameterized quasi-variational inequalities (2015)
  6. Bai, Lijie; Mitchell, John E.; Pang, Jong-Shi: Using quadratic convex reformulation to tighten the convex relaxation of a quadratic program with complementarity constraints (2014)
  7. Bai, Lijie; Mitchell, John E.; Pang, Jong-Shi: On convex quadratic programs with linear complementarity constraints (2013)
  8. Wu, Jia; Zhang, Liwei; Zhang, Yi: A smoothing Newton method for mathematical programs governed by second-order cone constrained generalized equations (2013)
  9. Stein, Oliver: Lifting mathematical programs with complementarity constraints (2012)
  10. Wu, Jia; Zhang, LiWei: A smoothing Newton method for mathematical programs constrained by parameterized quasi-variational inequalities (2011)
  11. Izmailov, A.F.; Solodov, M.V.: Examples of dual behaviour of Newton-type methods on optimization problems with degenerate constraints (2009)
  12. Giallombardo, Giovanni; Ralph, Daniel: Multiplier convergence in trust-region methods with application to convergence of decomposition methods for MPECs (2008)
  13. Lin, G.H.; Fukushima, M.: Hybrid approach with active set identification for mathematical programs with complementarity constraints (2006)
  14. Liu, Xinwei; Perakis, Georgia; Sun, Jie: A robust SQP method for mathematical programs with linear complementarity constraints (2006)
  15. Tao, Yan: Newton-type method for a class of mathematical programs with complementarity constraints (2006)
  16. Jian, Jinbao: A superlinearly convergent implicit smooth SQP algorithm for mathematical programs with nonlinear complementarity constraints (2005)
  17. Zhang, J.Z.; Liu, G.S.; Wang, S.Y.: A globally convergent approximately active search algorithm for solving mathematical programs with linear complementarity constraints (2004)
  18. Jiang, Houyuan; Ralph, Daniel: OPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints (1999)