Singular Riemannian barrier methods and gradient-projection dynamical systems for constrained optimization

DOI10.1080/02331930412331327184zbMath1153.34312OpenAlexW2067952903WikidataQ115301407 ScholiaQ115301407MaRDI QIDQ4669783

Hedy Attouch, Jérôme Bolte, Patrick Redont, Marc Teboulle

Publication date: 15 April 2005

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930412331327184

zbMATH Keywords

Dynamical systemsAsymptotic analysisBregman distancesBarrier methods in constrained optimizationContinuous gradient methodConvex Legendre functionsSingular Hessian Riemannian metric

Mathematics Subject Classification ID

Nonlinear programming (90C30) Ordinary differential inclusions (34A60) Evolution inclusions (34G25) Dynamical systems in control (37N35) Dynamical systems in optimization and economics (37N40)

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Cites Work

• Regularized Lotka-Volterra dynamical system as continuous proximal-like method in optimization.
• Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions
• A class of nonlinear elliptic—parabolic equations with time-dependent constraints
• Central Paths, Generalized Proximal Point Methods, and Cauchy Trajectories in Riemannian Manifolds
• Variational Analysis
• Barrier Operators and Associated Gradient-Like Dynamical Systems for Constrained Minimization Problems
• Hessian Riemannian Gradient Flows in Convex Programming
• Weak convergence of the sequence of successive approximations for nonexpansive mappings

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