The Mordukhovich Subdifferentials and Directions of Descent

P. D. Khanh (), J.-C. Yao () and N. D. Yen ()
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P. D. Khanh: University of Pedagogy of Ho Chi Minh City
J.-C. Yao: China Medical University
N. D. Yen: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 2, No 9, 518-534

Abstract: Abstract The problem of finding minima of weakly sequentially lower semicontinuous functions on reflexive Banach spaces is studied by means of convex and nonconvex subdifferentials. Finding a descent direction for a non-stationary point is a question of importance for many optimization algorithms. The existence or non-existence of such a direction is clarified through several theorems and a series of selective examples. For the general problem, a notion called radius of descent is proposed and shown to be useful for the analysis related to descent directions.

Keywords: Weakly sequentially lower semicontinuous function; Minimization; Subdifferential; Descent direction; Radius of descent; 49J52; 49J53; 90C26; 49J45 (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-015-0774-0

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