Related papers: Technical Note: PDE-constrained Optimization Formu…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must…
Modeling of brain tumor dynamics has the potential to advance therapeutic planning. Current modeling approaches resort to numerical solvers that simulate the tumor progression according to a given differential equation. Using…
Existing approaches to modeling the dynamics of brain tumor growth, specifically glioma, employ biologically inspired models of cell diffusion, using image data to estimate the associated parameters. In this work, we propose an alternative…
In anti-cancer drug development, a major scientific challenge is disentangling the complex relationships between high-dimensional genomics data from patient tumor samples, the corresponding tumor's organ of origin, the drug targets…
In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, introduced in [G. Cavalleri, P. Colli, A. Miranville, E. Rocca,…
We propose a method for extracting physics-based biomarkers from a single multiparametric Magnetic Resonance Imaging (mpMRI) scan bearing a glioma tumor. We account for mass effect, the deformation of brain parenchyma due to the growing…
Differential Evolution (DE) is a highly successful population based global optimisation algorithm, commonly used for solving numerical optimisation problems. However, as the complexity of the objective function increases, the wall-clock…
The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…
Early detection and quantification of tumour growth would help clinicians to prescribe more accurate treatments and provide better surgical planning. However, the multifactorial and heterogeneous nature of lung tumour progression hampers…
It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are…
Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification of efficient optimization algorithms. In this paper we propose and investigate…
PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…
In this paper, we develop an analytical framework for the partial differential equation underlying the consensus-based optimization model. The main challenge arises from the nonlinear, nonlocal nature of the consensus point, coupled with a…
In this paper, we address an optimal distributed control problem for a non-local model of phase-field type, describing the evolution of tumour cells in presence of a nutrient. The model couples a non-local and viscous Cahn-Hilliard equation…
We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…