## Mathematical Programs with Equilibrium ConstraintsThis book provides a solid foundation and an extensive study for Mathematical Programs with Equilibrium Constraints (MPEC). It begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalization, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions. The book also describes several iterative algorithms such as a penalty based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modeling of many practical problems. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

Mathematical Programs with Equilibrium Constraints Zhi-Quan Luo,Jong-Shi Pang,Daniel Ralph Limited preview - 1996 |

Mathematical Programs with Equilibrium Constraints Zhi-Quan Luo,Jong-Shi Pang,Daniel Ralph No preview available - 1996 |

Mathematical Programs with Equilibrium Constraints Zhi-Quan Luo,Jong-Shi Pang,Daniel Ralph No preview available - 1996 |

### Common terms and phrases

affine algorithm assume assumption bilevel program compact constant continuously differentiable convergence convex copositive Corollary CRCQ critical cone deduce defined denote directional derivative discussion dx,dy equation equivalent error bound exact penalty function feasible region finite formulation function y(x given global Hence homeomorphism implicit function implies index sets iterate Lemma LICQ linear program linearly Lipschitz continuous matrix Me(x minimize f(x minimize f(x,y Moreover MPAEC MPEC multiplier NCP constrained MP neighborhood nonempty nonlinear complementarity problem nonlinear program nonnegative nonsingular normal map notation null space objective function obtain optimal solution optimality conditions optimization problem pair parametric PC1 function penalty function piecewise PIPA2 polyhedron positive definite Proof Proposition quadratic program satisfying SBCQ SCOC second-order sequence SMFCQ solution function solving stationary point subanalytic subset sufficient conditions tangent cone Theorem tion unique solution variables variational inequalities vector