Methods for Solving Ill-Posed Extremum Problems with Optimal and Extra-Optimal Properties
| Autor: | Alexander S. Leonov |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Well-posed problem
Mathematical optimization Property (philosophy) General Mathematics media_common.quotation_subject 010102 general mathematics Estimator 02 engineering and technology 01 natural sciences 020303 mechanical engineering & transports 0203 mechanical engineering Consistency (statistics) A priori and a posteriori Quality (business) Physics::Chemical Physics 0101 mathematics Mathematics media_common |
| Zdroj: | Mathematical Notes. 105:385-397 |
| ISSN: | 1573-8876 0001-4346 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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