Search results for " and Control"
showing 10 items of 385 documents
Ovarian cancer susceptibility alleles and risk of ovarian cancer in BRCA1 and BRCA2 mutation carriers
2012
Germline mutations in BRCA1 and BRCA2 are associated with increased risks of breast and ovarian cancer. A genome-wide association study (GWAS) identified six alleles associated with risk of ovarian cancer for women in the general population. We evaluated four of these loci as potential modifiers of ovarian cancer risk for BRCA1 and BRCA2 mutation carriers. Four single-nucleotide polymorphisms (SNPs), rs10088218 (at 8q24), rs2665390 (at 3q25), rs717852 (at 2q31), and rs9303542 (at 17q21), were genotyped in 12,599 BRCA1 and 7,132 BRCA2 carriers, including 2,678 ovarian cancer cases. Associations were evaluated within a retrospective cohort approach. All four loci were associated with ovarian …
Geometric Optimal Control of the Generalized Lotka-Volterra Model of the Intestinal Microbiome
2022
We introduce the theoretical framework from geometric optimal control for a control system modeled by the Generalized Lotka-Volterra (GLV) equation, motivated by restoring the gut microbiota infected by Clostridium difficile combining antibiotic treatment and fecal injection. We consider both permanent control and sampled-data control related to the medical protocols.
Regularity of sets under a reformulation in a product space of reduced dimension
2023
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility problems defined by finitely many sets, some other require the use of a product space reformulation to construct equivalent problems with two sets. In this work we analyze how some regularity properties are preserved under a reformulation in a product space of reduced dimension. This allows us to establish local linear convergence of parallel projection methods which are constructed through this reformulation.
Monge Problem on infinite dimensional Hilbert space endowed with suitable Gaussian measure
2014
In this paper we solve the Monge problem on infinite dimensional Hilbert space endowed with a suitable Gaussian measure, that satisfies the Lebesgue differentiation theorem.
A globally convergent and locally quadratically convergent modified B-semismooth Newton method for $\ell_1$-penalized minimization
2015
We consider the efficient minimization of a nonlinear, strictly convex functional with $\ell_1$-penalty term. Such minimization problems appear in a wide range of applications like Tikhonov regularization of (non)linear inverse problems with sparsity constraints. In (2015 Inverse Problems (31) 025005), a globalized Bouligand-semismooth Newton method was presented for $\ell_1$-Tikhonov regularization of linear inverse problems. Nevertheless, a technical assumption on the accumulation point of the sequence of iterates was necessary to prove global convergence. Here, we generalize this method to general nonlinear problems and present a modified semismooth Newton method for which global converg…
On optimal control of free boundary problems of obstacle type
2018
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed domain. The discretized optimal control problem is a non-smooth and non-convex mathematical programing problem. The performance of the standard BFGS quasi-Newton method and the BFGS method with the inexact line search are tested.
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
2020
This work is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuska-Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, …
Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems
2019
In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to lar…
Comparison of Numerical Methods in the Contrast Imaging Problem in NMR
2013
International audience; In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. A first synthesis of locally optimal solutions is given in the single-input case using geometric methods based on Pontryagin's maximum principle. We then compare these results using direct methods and a moment-based approach, and make a first step towards global optimality. Finally, some preliminary results are given in the bi-input case.
Recent Advances in Static Output-Feedback Controller Design with Applications to Vibration Control of Large Structures
2014
Published version of an article in the journal: Modeling, Identification and Control. Also available from the publisher at: http://dx.doi.org/10.4173/mic.2014.3.4 Open Access In this paper, we present a novel two-step strategy for static output-feedback controller design. In the first step, an optimal state-feedback controller is obtained by means of a linear matrix inequality (LMI) formulation. In the second step, a transformation of the LMI variables is used to derive a suitable LMI formulation for the static output-feedback controller. This design strategy can be applied to a wide range of practical problems, including vibration control of large structures, control of oshore wind turbine…