Related papers: Constrained Optimization for Liquid Crystal Equili…
This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system…
This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on the results of [14] for…
This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the Frank-Oseen elastic free-energy model of nematic and cholesteric liquid crystals, where the required unit-length…
This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…
We study a fictitious domain approach with Lagrange multipliers to discretize Stokes equations on a mesh that does not fit the boundaries. A mixed finite element method is used for fluid flow. Several stabilization terms are added to…
Multiple equilibrium states arise in many physical systems, including various types of liquid crystal structures. Having the ability to reliably compute such states enables more accurate physical analysis and understanding of experimental…
Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…
Motivated by a problem originating in the study of defect structures in nematic liquid crystals, we describe and study a numerical algorithm for the resolution of a Plateau-like problem. The energy contains the area of a two-dimensional…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…
The magnetostatic field distribution in a nonlinear medium amounts to the unique minimizer of the magnetic coenergy over all fields that can be generated by the same current. This is a nonlinear saddlepoint problem whose numerical solution…
This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…
Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that…
We investigate non-convex optimization problems in $BV(\Omega)$ with two-sided pointwise inequality constraints. We propose a regularization and penalization method to numerically solve the problem. Under certain conditions, weak limit…
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}$ and its degree of orientation $s$,…
This paper derives an a posteriori error estimator for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on previous results for…