Numerical solution of optimal control of atherosclerosis using direct and indirect methods with shooting/collocation approach

DOI10.1016/j.camwa.2022.08.047OpenAlexW4296613261MaRDI QIDQ2094343

M. R. Eslahchi, F. Nasresfahani

Publication date: 28 October 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.04148

zbMATH Keywords

collocation methodfree boundary problemparabolic equationfixed point methodatherosclerosisoptimal control of partial differential equation

Mathematics Subject Classification ID

Nonlinear programming (90C30) Optimality conditions for problems involving partial differential equations (49K20) Interior-point methods (90C51) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Cites Work

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• Nonmonotonic trust region algorithm
• Adjoint estimation from a direct multiple shooting method
• Interior-point methods for nonconvex nonlinear programming: jamming and numerical testing
• Application of fixed point-collocation method for solving an optimal control problem of a parabolic-hyperbolic free boundary problem modeling the growth of tumor with drug application
• Spectral methods for substantial fractional differential equations
• On the Newton interior-point method for nonlinear programming problems
• The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems
• A mathematical model for oncolytic virus spread using the telegraph equation
• Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the artery
• Analysis of control for a free boundary problem of steady plaques in the artery
• A free boundary problem for steady small plaques in the artery and their stability
• Optimal control oriented to therapy for a free-boundary tumor growth model
• A new Legendre operational technique for delay fractional optimal control problems
• Optimal control for a parabolic-hyperbolic free boundary problem modeling the growth of tumor with drug application
• A generalized multiscale finite element method (GMsFEM) for perforated domain flows with Robin boundary conditions
• Generalized Bessel functions: Theory and their applications
• Finite Element Approximation of Parabolic Time Optimal Control Problems
• A shooting method for solving two-point boundary-value problems arising from non-singular bang-bang optimal control problems
• Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
• Error Analysis of Fully Discrete Finite Element Approximations to an Optimal Control Problem Governed by a Time-Fractional PDE
• Finite difference scheme for automatic costate calculation
• Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
• Legendre pseudo-spectral method for optimal control problem governed by a time-fractional diffusion equation
• Space–time spectral collocation method for one-dimensional PDE constrained optimisation
• Fully Legendre Spectral Galerkin Algorithm for Solving Linear One-Dimensional Telegraph Type Equation
• A trust region method based on interior point techniques for nonlinear programming.