Regularized Lotka-Volterra dynamical system as continuous proximal-like method in optimization.

DOI10.1023/B:JOTA.0000037603.51578.45zbMath1076.90053OpenAlexW2029465407MaRDI QIDQ703163

Hedy Attouch, Marc Teboulle

Publication date: 11 January 2005

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/b:jota.0000037603.51578.45

zbMATH Keywords

global convergencerelative entropyLyapunov functionsDynamical systemsasymptotic analysisviabilityconvex minimizationcontinuous gradient methodimplicit discrete schemeinterior proximal algorithmsLotka-Volterra differential equationsregularized logarithmic barrier

Mathematics Subject Classification ID

Nonlinear programming (90C30) Interior-point methods (90C51) Ordinary differential inclusions (34A60) Stability of solutions to ordinary differential equations (34D20) Growth and boundedness of solutions to ordinary differential equations (34C11)

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Cites Work

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• On the convergence of the exponential multiplier method for convex programming
• Multiplicative iterative algorithms for convex programming
• Modified barrier functions (theory and methods)
• Asymptotic convergence of nonlinear contraction semigroups in Hilbert space
• A dynamical system associated with Newton's method for parametric approximations of convex minimization problems
• Nonlinear rescaling and proximal-like methods in convex optimization
• Optimization and dynamical systems
• A dynamical approach to convex minimization coupling approximation with the steepest descent method
• An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities
• The Nonlinear Geometry of Linear Programming. I Affine and Projective Scaling Trajectories
• Entropic Proximal Mappings with Applications to Nonlinear Programming
• Monotone Operators and the Proximal Point Algorithm
• Convergence of Proximal-Like Algorithms
• Proximal Minimization Methods with Generalized Bregman Functions
• Evolutionary Games and Population Dynamics
• On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces
• THE HEAVY BALL WITH FRICTION METHOD, I. THE CONTINUOUS DYNAMICAL SYSTEM: GLOBAL EXPLORATION OF THE LOCAL MINIMA OF A REAL-VALUED FUNCTION BY ASYMPTOTIC ANALYSIS OF A DISSIPATIVE DYNAMICAL SYSTEM
• Entropy-Like Proximal Methods in Convex Programming
• Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Convex Analysis