Nonlinear programming without a penalty function. (English) Zbl 1049.90088

Summary: In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a ”filter” is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of S\(\l_1\)QP.


90C30 Nonlinear programming
90C55 Methods of successive quadratic programming type
49M30 Other numerical methods in calculus of variations (MSC2010)


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