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A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints. (English) Zbl 0966.65052
A 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.

MSC:
65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
90C26 Nonconvex programming, global optimization
90C51 Interior-point methods
Software:
TRICE
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