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Failure of global convergence for a class of interior point methods for nonlinear programming. (English) Zbl 0963.65063
The authors consider nonlinear nonconvex optimization problems of the form $\min_{x\in\mathbb{R}^n} f(x),\quad c(x)= 0,\quad x_i\geq 0.$ For these problems, they demonstrate that a class of interior point methods is not globally convergent. It is shown that these algorithms produce limit points that are neither feasible nor stationary points.

##### MSC:
 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 90C51 Interior-point methods
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