Abstract
This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualification is required. The optimality conditions are formulated in such a way that the gaps between the necessary and sufficient conditions are small and even vanish completely under mild constraint qualifications.
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Communicated by O. L. Mangasarian
This paper is dedicated to the memory of W. Wetterling.
The authors would like to thank Wolfgang Wetterling and Frank Twilt for fruitful discussions and an anonymous referee for many valuable comments.
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Still, G., Streng, M. Optimality conditions in smooth nonlinear programming. J Optim Theory Appl 90, 483–515 (1996). https://doi.org/10.1007/BF02189792
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DOI: https://doi.org/10.1007/BF02189792