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Titlebook: Algorithms for Constrained Minimization of Smooth Nonlinear Functions; A. G. Buckley,J.- L. Goffin Book 1982Latest edition Springer-Verlag

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Determining feasibility of a set of nonlinear inequality constraints,imates are used. We also demonstrate that with certain choices of the penalty function, our algorithm will produce points which are as feasible as possible, on feasible problems. Some computational results are also presented.
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https://doi.org/10.1007/978-3-662-45207-3 that it can give large gains in efficiency when a sequence of steps has to follow a curved constraint boundary, and it provides some highly useful algorithms with a Q-superlinear rate of convergence. The watchdog technique is described and discussed, and some global and Q-superlinear convergence properties are proved.
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https://doi.org/10.1007/978-3-322-84998-4and a feasibility improving direction; an exact penalty function is used to determine the stepsize. The method can be viewed as an efficient approximation to the quasi-Newton along geodesics of [1] where feasibility was enforced at each step. Its relation with multiplier methods and recursive quadratic programming methods is also investigated.
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https://doi.org/10.1007/978-3-322-84998-4 incorporates a rule for choosing the penalty parameter and, near a solution, employs a search are rather than a search direction to avoid truncation of the step length, and thereby loss of superlinear convergence.
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The watchdog technique for forcing convergence in algorithms for constrained optimization, that it can give large gains in efficiency when a sequence of steps has to follow a curved constraint boundary, and it provides some highly useful algorithms with a Q-superlinear rate of convergence. The watchdog technique is described and discussed, and some global and Q-superlinear convergence properties are proved.
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