Interior quasi-subgradient method with non-Euclidean distances for constrained quasi-convex optimization problems in hilbert spaces

Regina S. Burachik (), Yaohua Hu () and Xiaoqi Yang ()
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Regina S. Burachik: UniSA STEM, University of South Australia
Yaohua Hu: Shenzhen University
Xiaoqi Yang: The Hong Kong Polytechnic University

Journal of Global Optimization, 2022, vol. 83, issue 2, No 5, 249-271

Abstract: Abstract An interior quasi-subgradient method is proposed based on the proximal distance to solve constrained nondifferentiable quasi-convex optimization problems in Hilbert spaces. It is shown that a newly introduced generalized Gâteaux subdifferential is a subset of a quasi-subdifferential. The convergence properties, including the global convergence and iteration complexity, are investigated under the assumption of the Hölder condition of order p, when using the constant/diminishing/dynamic stepsize rules. Convergence rate results are obtained by assuming a Hölder-type weak sharp minimum condition relative to an induced proximal distance.

Keywords: Quasi-convex optimization; Interior subgradient method; Proximal distance; Convergence analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-021-01110-2

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