Iteration Functions in Some Nonsmooth Optimization Algorithms

✍ Scribed by Guoshan Liu

• Book ID: 102595218
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 241 KB
• Volume: 211
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5450

✦ Synopsis

In this paper, it is proved that a locally Lipschitzian function has a PHR iteration function or a QS iteration function if and only if it is pseudo-regular, and a locally Lipschitzian function has a positive homogeneous PHR iteration function or a positive homogeneous QS iteration function if and only if it is continuously differentiable. In addition, we also give the computable PHR iteration functions or QS iteration functions for a piece-wise smooth function and a subsmooth function, respectively.