In this paper we propose an inexact proximal point method to solve constrained minimization problems with locally Lipschitz quasiconvex objective functions. Assuming that the function is also bounded from below, lower semicontinuous and using proximal distances, we show that the sequence generated for the method converges to a stationary point of the problem.
Bibliographical noteFunding Information:
The authors are grateful to Zuly Salinas (Master Student of the Israel Institute of Technology-Israel) and Nguyen Bao Tran (Doctoral Student of the Center for Mathematical Modeling CMM-Chile University) for the continuous communication with the second author on inexact proximal point methods for convex functions. The research of the first author was supported by the Postdoctoral Scholarship CAPES-FAPERJ Edital PAPD-2011.
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- Computing science
- Global optimization
- Nonlinear programming
- Proximal point methods
- Quasiconvex minimization