Accelerated methods for weakly-quasi-convex optimization problems

Sergey Guminov (), Alexander Gasnikov () and Ilya Kuruzov ()
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Sergey Guminov: National Research University Higher School of Economics
Alexander Gasnikov: Moscow Institute of Physics and Technology
Ilya Kuruzov: Moscow Institute of Physics and Technology

Computational Management Science, 2023, vol. 20, issue 1, No 36, 19 pages

Abstract: Abstract We provide a quick overview of the class of $$\alpha$$ α -weakly-quasi-convex problems and its relationships with other problem classes. We show that the previously known Sequential Subspace Optimization method retains its optimal convergence rate when applied to minimization problems with smooth $$\alpha$$ α -weakly-quasi-convex objectives. We also show that Nemirovski’s conjugate gradients method of strongly convex minimization achieves its optimal convergence rate under weaker conditions of $$\alpha$$ α -weak-quasi-convexity and quadratic growth. Previously known results only capture the special case of 1-weak-quasi-convexity or give convergence rates with worse dependence on the parameter $$\alpha$$ α .

Keywords: Non-convex minimization; First-order methods; Accelerated methods (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10287-023-00468-w

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