## Iterative methods for solving linear complementarity and linear programming problems |

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### Contents

SOME ITERATIVE METHODS FOR SOLVING NONLINEAR | 8 |

ITERATIVE METHODS FOR SOLVING SYMMETRIC | 33 |

ITERATIVE METHODS FOR SOLVING NONSYMMMETRIC | 55 |

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### Common terms and phrases

accumulation point approximate solution Armijo stepsize rule augmented Lagrangian method closed convex set constraint qualification convex function diagonal matrix dual linear program feasible region following theorem formulation function f go to step gradient projection method Hence iterative methods Karush-Kuhn-Tucker conditions least norm Lemma Let f Let the matrix linear complementarity problem linear program 5.1.1 linear programming problem Lipschitz continuous Mangasarian 81 methods for solving Minimize f(x Mx q nondegenerate nondifferentiable nonempty closed convex nonlinear complementarity problem nonsymmetric objective function value P-matrix perturbation point which solves positive semidefinite matrix primal problem projected Jacobi method projected SOR method Proof prove the convergence proximal point algorithm pseudo-convex quadratic program sequence converging set Q sharp minimum small positive tolerance solves the dual solves the following solves the LCP solves the problem solving the linear subgradient method symmetric positive semidefinite test problem thesis unique solution Vf(x x e Q xT(Mx+q