Related papers: Technical Note: PDE-constrained Optimization Formu…
In this paper, a free boundary problem modelling the growth of tumor is considered. The model includes two reaction-diffusion equations modelling the diffusion of nutrient and drug in the tumor and three hyperbolic equations describing the…
The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Tumor growth prediction, a highly challenging task, has long been viewed as a mathematical modeling problem, where the tumor growth pattern is personalized based on imaging and clinical data of a target patient. Though mathematical models…
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…
We study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor…
We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
Parameters in mathematical models for glioblastoma multiforme (GBM) tumour growth are highly patient specific. Here we aim to estimate parameters in a Cahn-Hilliard type diffuse interface model in an optimised way using model order…
Computational systems and methods are often being used in biological research, including the understanding of cancer and the development of treatments. Simulations of tumor growth and its response to different drugs are of particular…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply, and chemotherapy. The subdiffusion of the system…
We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-dimensional random parameters. To address the critical…
The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by…
This paper introduces a method for estimating the shape and location of an embedded tumor. The approach utilizes shape optimization techniques, applying the coupled complex boundary method. By rewriting the problem -- characterized by a…
Optimization algorithms are increasingly being used in applications with limited time budgets. In many real-time and embedded scenarios, only a few iterations can be performed and traditional convergence metrics cannot be used to evaluate…
We study deterministic and stochastic primal-dual sub-gradient algorithms for distributed optimization of a separable objective function with global inequality constraints. In both algorithms, the norm of the Lagrangian multipliers are…
This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…