Related papers: A regularized penalty-multiplier method for approx…
We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…
This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…
In this paper, we focus on a class of constrained nonlinear optimization problems (NLP), where some of its equality constraints define a closed embedded submanifold $\mathcal{M}$ in $\mathbb{R}^n$. Although NLP can be solved directly by…
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…
This paper is concerned with the regularity of shape optimizers of a class of isoperimetric problems under convexity constraint. We prove that minimizers of the sum of the perimeter and a perturbative term, among convex shapes, are C…
We consider the minimization of $\int_{\Omega_{\ep}} |D\vec u|^p \dd\vec x$ in a perforated domain $\Omega_{\ep}:= \Omega \setminus \bigcup_{i=1}^M B_{\ep}(\vec a_i)$ of $\R^n$, among maps $\vec u \in W^{1,p}(\Omega_{\ep}, \R^n)$ that are…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous…
We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…
We introduce numerical methods for the approximation of the main (global) quantities in Pluripotential Theory as the \emph{extremal plurisubharmonic function} $V_E^*$ of a compact $\mathcal L$-regular set $E\subset \C^n$, its…
A new approach for reducing error of the volume penalization method is proposed. The mask function is modified by shifting the interface between solid and fluid by ({\nu}{\eta})^0.5 toward the fluid region, where {\nu} and {\eta} are the…
Given $\Omega$ bounded open set of $\mathbb R^{n}$ and $\alpha\in \mathbb R$, let us consider \[ \mu(\Omega,\alpha)=\min_{\substack{v\in W_{0}^{1,2}(\Omega)\\v\not\equiv 0}} \frac{\displaystyle\int_{\Omega} |\nabla v|^{2}dx+\alpha…
The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…
This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these methods when the necessary unit-length constraint is…
We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for…
In this paper, we provide a candidate solution to obtain the coefficients of the conformal mapping for a lower half plane containing a symmetrical noncircular cavity using penalty function method and modified Particle Swarm Method. The…
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…
Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries are available. The commonly used Brinkman-volume-penalization models geometries as porous…
Newton's method for finding an unconstrained minimizer for strictly convex functions, generally speaking, does not converge from any starting point. We introduce and study the damped regularized Newton's method (DRNM). It converges globally…