Using dynamical systems methods to solve minimization problems

DOI10.1016/0168-9274(95)00065-3zbMath0837.65065OpenAlexW2020926303MaRDI QIDQ1902083

Johannes Schropp

Publication date: 14 November 1995

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00065-3

zbMATH Keywords

convergenceminimization problemsnumerical examplesdynamical systemomega-limit setone-step methodsgradient differential equationMichaelis-Menten kinetics model

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Numerical methods for initial value problems involving ordinary differential equations (65L05) Dynamical systems and ergodic theory (37-XX)

Related Items (14)

Dynamical Analysis of Continuous Higher-Order Hopfield Networks for Combinatorial Optimization ⋮ Continuous analog of accelerated OS-EM algorithm for computed tomography ⋮ A dynamical system method for solving nonlinear ill-posed problems ⋮ A second-order pseudo-transient method for steady-state problems ⋮ Convergence analysis of the Levenberg–Marquardt method ⋮ Continuous-time image reconstruction using differential equations for computed tomography ⋮ Explicit pseudo-transient continuation and the trust-region updating strategy for unconstrained optimization ⋮ A trajectory-based method for constrained nonlinear optimization problems ⋮ Tomographic inverse problem with estimating missing projections ⋮ Continuous-time method and its discretization to inverse problem of intensity-modulated radiation therapy treatment planning ⋮ Combining trust-region techniques and Rosenbrock methods to compute stationary points ⋮ Dose-volume constrained optimization in intensity-modulated radiation therapy treatment planning ⋮ Discretization of implicit ODEs for singular root-finding problems ⋮ One- and multistep discretizations of index 2 differential algebraic systems and their use in optimization

Cites Work

• Discrete evolutions: Convergence and applications
• On invariant closed curves for one-step methods
• Invariant curves for numerical methods
• On the Numerical Approximation of Phase Portraits Near Stationary Points
• Spurious solutions of numerical methods for initial value problems
• Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems
• A Reduction Principle for ω‐Limit Sets
• Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
• An exact sequence in differential topology
• Implicit Runge-Kutta Processes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Using dynamical systems methods to solve minimization problems