Constrained extremum problems, regularity conditions and image space analysis. I: The scalar finite-dimensional case. (English) Zbl 1398.49034
Summary: Image space analysis has proved to be instrumental in unifying several theories, apparently disjoint from each other. With reference to constraint qualifications/regularity conditions in optimization, such an analysis has been recently introduced by Moldovan and Pellegrini. Based on this result, the present paper is a preliminary part of a work, which aims at exploiting the image space analysis to establish a general regularity condition for constrained extremum problems. The present part deals with scalar constrained extremum problems in a Euclidean space. The vector case as well as the case of infinite-dimensional image will be the subject of subsequent papers.
For Part II, see [L. Pellegrini and the author, ibid. 177, No. 3, 788–810 (2018; Zbl 1398.49033)].
For Part II, see [L. Pellegrini and the author, ibid. 177, No. 3, 788–810 (2018; Zbl 1398.49033)].
MSC:
| 49N60 | Regularity of solutions in optimal control |
| 90C30 | Nonlinear programming |
| 90C46 | Optimality conditions and duality in mathematical programming |
Citations:
Zbl 1398.49033References:
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