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The paper presents an algorithm for solving nonlinear programming problems. The algorithm is based on the combination of interior and exterior point methods. The latter is also known as the primaldual nonlinear rescaling method. The paper shows that in certain cases when the interior point method (ipm) fails to achieve the solution with the high level of accuracy, the use of the exterior point method (epm) can remedy this situation. The result is demonstrated by solving problems from cops anddoi:10.1023/b:coap.0000042029.73199.83 fatcat:ofl25puaevafhlvsorvsshtcuq