Methods for Solving Ill-Posed Extremum Problems with Optimal and Extra-Optimal Properties

被引：0
|
作者：
A. S. Leonov
机构：
[1] National Research Nuclear University “MEPhI”,
来源：
Mathematical Notes | 2019年 / 105卷
关键词：
ill-posed extremum problems; regularizing algorithms; quality of approximate solution; a posteriori estimate of quality; regularizing algorithm of extra-optimal quality;
D O I：
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中图分类号：
学科分类号：
摘要：
The notion of the quality of approximate solutions of ill-posed extremum problems is introduced and a posteriori estimates of quality are studied for various solution methods. Several examples of quality functionals which can be used to solve practical extremum problems are given. The new notions of the optimal, optimal-in-order, and extra-optimal qualities of a method for solving extremum problems are defined. A theory of stable methods for solving extremum problems (regularizing algorithms) of optimal-in-order and extra-optimal quality is developed; in particular, this theory studies the consistency property of a quality estimator. Examples of regularizing algorithms of extra-optimal quality for solving extremum problems are given.
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页码：385 / 397
页数：12
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