Abstract
In this paper, we introduce a concept of substationary points and present a new trust region-based method for the optimization problems with general nonlinear equality constraints and simple bounds. Without the linear independent assumption on the gradients of the equalitiy constraints, we prove the global convergence results for the main algorithm and indicate that they extend the results on SQP and those on trust region methods for equality constrained optimization and for optimization with simple bounds. Moreover, since any nonlinear programming problem can be converted into the standard nonlinear programming by introducing slack variables, the trust region method presented in this paper can be used for solving general nonlinear programming problems.
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This work is supported by the National Natural Science Foundation of China and the Management, Decision and Information System Lab, the Chinese Academy of Sciences.
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Zhongwen, C., Jiye, H. & Qiaoming, H. A globally convergent trust region algorithm for optimization with general constraints and simple bounds. Acta Mathematicae Applicatae Sinica 15, 425–432 (1999). https://doi.org/10.1007/BF02684044
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DOI: https://doi.org/10.1007/BF02684044