Lifts of Non-Compact Convex Sets and Cone Factorizations
| Autor: | Lihong Zhi, Chu Wang |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Regular polygon Convex set 02 engineering and technology Combinatorics Lift (mathematics) symbols.namesake 020901 industrial engineering & automation Factorization Optimization and Control (math.OC) Recession cone Weierstrass factorization theorem FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) symbols 020201 artificial intelligence & image processing Affine transformation Mathematics - Optimization and Control Information Systems Mathematics |
| Zdroj: | Journal of Systems Science and Complexity. 33:1632-1655 |
| ISSN: | 1559-7067 1009-6124 |
| DOI: | 10.1007/s11424-020-9050-y |
| Popis: | This paper generalizes the factorization theorem of Gouveia, Parrilo and Thomas to a broader class of convex sets. Given a general convex set, the authors define a slack operator associated to the set and its polar according to whether the convex set is full dimensional, whether it is a translated cone and whether it contains lines. The authors strengthen the condition of a cone lift by requiring not only the convex set is the image of an affine slice of a given closed convex cone, but also its recession cone is the image of the linear slice of the closed convex cone. The authors show that the generalized lift of a convex set can also be characterized by the cone factorization of a properly defined slack operator. |
| Databáze: | OpenAIRE |
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