The multiobjective steepest descent direction is not Lipschitz continuous, but is Hölder continuous
| Autor: | Benar Fux Svaiter |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Polynomial
021103 operations research Applied Mathematics 0211 other engineering and technologies Hölder condition 010103 numerical & computational mathematics 02 engineering and technology Management Science and Operations Research Lipschitz continuity 01 natural sciences Industrial and Manufacturing Engineering Exponent Applied mathematics Vector field 0101 mathematics Gradient descent Software Mathematics |
| Zdroj: | Operations Research Letters. 46:430-433 |
| ISSN: | 0167-6377 |
| DOI: | 10.1016/j.orl.2018.05.008 |
| Popis: | The aim of this manuscript is to characterize the continuity properties of the multiobjective steepest descent direction (vector field) for smooth objective functions. We will show that this vector field is Holder continuous with optimal exponent 1/2. In particular, this vector field fails to be Lipschitz continuous even for polynomial objectives. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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