Subdifferentials at infinity and applications in optimization.
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| Title: | Subdifferentials at infinity and applications in optimization. |
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| Authors: | Kim, Do Sang1 (AUTHOR) dskim@pknu.ac.kr, Nguyen, Minh Tùng2 (AUTHOR) tungnm@hub.edu.vn, Pham, Tien-Son3 (AUTHOR) sonpt@dlu.edu.vn |
| Source: | Mathematical Programming. Nov2025, Vol. 214 Issue 1/2, p409-440. 32p. |
| Subjects: | Mathematical optimization, Infinity (Mathematics), Cones, Subdifferentials, Lipschitz continuity |
| Abstract: | In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions are established. A complete characterization of the Lipschitz continuity at infinity for lower semicontinuous functions is given. The obtained results are aimed ultimately at applications to diverse problems of optimization, such as optimality conditions, coercive properties, weak sharp minima and stability results. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions are established. A complete characterization of the Lipschitz continuity at infinity for lower semicontinuous functions is given. The obtained results are aimed ultimately at applications to diverse problems of optimization, such as optimality conditions, coercive properties, weak sharp minima and stability results. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 00255610 |
| DOI: | 10.1007/s10107-024-02187-9 |
