Geodesic
Methods for solving ill-posed extremum problems with optimal and extra-optimal quality
Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 406-420

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The concept of the quality of approximate solutions of ill-posed extremum problems is introduced and a posteriori quality estimates for various solution methods are studied. Examples of quality functionals are given, which can be used to solve practical extremum problems. New concepts of optimal, optimal in order and extra-optimal quality of the method for solving the extremum problem are determined. The theory of stable methods for solving extremum problems (regularizing algorithms) with optimal order and extra optimal quality is developed, in which, in particular, the property of consistency of the evaluation function of quality is studied. Examples of regularizing algorithms with extra-optimal quality of solutions for extremal problems are given.
Keywords: ill-posed extremum problems, regularizing algorithms, quality of approximate solution, a posteriori estimate of quality, regularizing algorithm of extra-optimal quality. 
@article{MZM_2019_105_3_a7,
     author = {A. S. Leonov},
     title = {Methods for solving ill-posed extremum problems with optimal and extra-optimal quality},
     journal = {Matemati\v{c}eskie zametki},
     pages = {406--420},
     publisher = {mathdoc},
     volume = {105},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a7/}
}
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A. S. Leonov. Methods for solving ill-posed extremum problems with optimal and extra-optimal quality. Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 406-420. http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a7/