Linearization and Gap Function in Nonsmooth Quasiconvex Optimization Using Incident Subdifferential

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Soroush Hamed

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Journal Paper

Paper Information

Journal: CONTROL AND OPTIMIZATION IN APPLIED MATHEMATICS Year:2022 | Volume:7 | Issue:1 Page(s): 79-92

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Title

Linearization and Gap Function in Nonsmooth Quasiconvex Optimization Using Incident Subdifferential

Author(s)

Soroush Hamed | Issue Writer Certificate

Keywords

Quasiconvex optimization

Linearization

Gap function

Incident subdifferential

Abstract

The purpose of this paper is to develop nonsmooth optimization problems (P) in which all emerging functions are assumed to be real-valued quasiconvex functions that are defined on a finite-dimensional Euclidean space. First, we introduce two linear optimization problems with the same optimal value of the considered problem. Then, we introduce a real-valued non-negative Gap function for (P), and we provide some conditions which ensure that its null points are the same as the optimal solution of problem (P). The results are based on Incident subdifferential, which is an important concept in the analysis of quasiconvex functions.

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APA: Copy

Soroush, Hamed. (2022). Linearization and Gap Function in Nonsmooth Quasiconvex Optimization Using Incident Subdifferential. CONTROL AND OPTIMIZATION IN APPLIED MATHEMATICS, 7(1), 79-92. SID. https://sid.ir/paper/1058284/en

Vancouver: Copy

Soroush Hamed. Linearization and Gap Function in Nonsmooth Quasiconvex Optimization Using Incident Subdifferential. CONTROL AND OPTIMIZATION IN APPLIED MATHEMATICS[Internet]. 2022;7(1):79-92. Available from: https://sid.ir/paper/1058284/en

IEEE: Copy

Hamed Soroush, “Linearization and Gap Function in Nonsmooth Quasiconvex Optimization Using Incident Subdifferential,” CONTROL AND OPTIMIZATION IN APPLIED MATHEMATICS, vol. 7, no. 1, pp. 79–92, 2022, [Online]. Available: https://sid.ir/paper/1058284/en

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