A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints.

*(English)*Zbl 0966.65052A trust region and affine scaling interior point method (TRAM) is proposed for a general nonlinear minimization with linear inequality constraints. A Newton step is derived from the complementarity conditions. Based on this Newton step, a trust region subproblem is formed and the original objective function is monotonically decreased. Explicit sufficient decrease conditions are proposed for satisfying the first-order and second-order necessary conditions.

There are global and local convergence properties of the proposed trust region and affine scaling interior point method. It is shown that the proposed explicit decrease conditions are sufficient for satisfying complementarity, dual feasibility and second-order necessary conditions, respectively. It is also established that a trust region solution is asymptotically in the interior of the proposed trust region subproblem.

There are global and local convergence properties of the proposed trust region and affine scaling interior point method. It is shown that the proposed explicit decrease conditions are sufficient for satisfying complementarity, dual feasibility and second-order necessary conditions, respectively. It is also established that a trust region solution is asymptotically in the interior of the proposed trust region subproblem.

Reviewer: Stefan Mititelu (Bucureşti)

##### MSC:

65K05 | Numerical mathematical programming methods |

90C06 | Large-scale problems in mathematical programming |

90C26 | Nonconvex programming, global optimization |

90C51 | Interior-point methods |