arXiv subjects

Aziz Belmiloudi

Publications and source records attributed to Aziz Belmiloudi.

3 recordsLinked to original sources

arXiv2026

Optimal Control Problem with Mixed Control and State Constraints for Cancer Chemotherapy and Treatment Optimization

The success of chemotherapy depends on the effectiveness of the drug delivery strategy and its ability to destroy cancer cells while minimizing damage to healthy tissues. The main objective of this work is to minimize the density of invasive tumour cells by controlling the chemotherapeutic agents. For this, we address an optimal control problem with mixed control and state constraints. The concentration of chemotherapeutic drugs is represented as a control variable. We use a nonlinear reaction-diffusion equation to describe the effect of drugs on the progression of invasive tumours. We start with the mathematical analysis of this initial boundary value problem. Then, we formulate the optimal control problem, explain the role of different constraints, and derive first-order necessary conditions of optimality. Finally, in order to demonstrate the efficiency of the proposed strategy, numerical simulations in the case of the eradication of malignant lung tumours, are presented and analysed.

math.OC↗

arXiv2019

Optimal Control for Chemotaxis Systems and Adjoint-Based Optimization with Multiple-Relaxation-Time Lattice Boltzmann Models

This paper is devoted to continuous and discrete adjoint-based optimization approaches for optimal control problems governed by an important class of Nonlinear Coupled Anisotropic Convection-Diffusion Chemotaxis-type System (NCACDCS). This study is motivated by the fact that the considered complex systems (with complex geometries) appear in diverse biochemical, biological and biosocial criminology problems. To solve numerically the corresponding nonlinear optimization problems, the primal problem NCACDCS is discretised by a coupled Lattice Boltzmann Method with a general Multiple-Relaxation-Time collision operators (MRT) while for the adjoint problem, an Adjoint Multiple-Relaxation-Time lattice Boltzmann model (AMRT) is proposed and investigated. First, the optimal control problems are formulated and first-order necessary optimality conditions are established by using sensitivity and adjoint calculus. The resulting problems are discretised by the coupled MRT and AMRT models and solved via gradient descent methods. First of all, an efficient and stable modified MRT model for NCACDCS is developed, and through the Chapman-Enskog analysis we show that NCACDCS can be correctly recovered from the proposed MRT model. For the adjoint problem, the discretisation strategy is based on AMRT model, which is found to be as simple as MRT model with also highly-efficient parallel nature. The derivation of AMRT model and the discrete cost functional gradient are derived mathematically in detail using the developed MRT model. The obtained method is reliable, efficient, practical to implement and can be easily incorporated into any existing MRT code.

math.OC↗

arXiv2018

Error and stability analysis of an anisotropic phase-field model for binary-fluid mixtures in the presence of magnetic-field

In this article, we study the error and stability of the proposed numerical scheme in order to solve a two dimensional anisotropic phase-field model with convection and externally applied magnetic field in an isothermal solidification of binary alloys. The proposed numerical scheme is based on mixed finite element method satisfying the CFL condition. A particular application with real physical parameters of Nickel-Copper(Ni-Cu) is considered in order to validate the numerical scheme employed. The results of stability and error analysis substantiates complete accordance with the postulated theoretical error estimates which demonstrates the efficiency of the presented method.

math.NA↗