Related papers: Uniqueness and Stability of Optimizers for a Membr…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
We present a model for pore stabilization in membranes without surface tension. Whereas an isolated pore is always unstable (since it either shrinks tending to re-seal or grows without bound til to membrane disintegration), it is shown that…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
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…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows to determine the singularity structure of the solutions. The result is applied to braneworlds…
In this paper we consider a minimization problem of the type $$ I_{\beta,p}(D;\Omega)=\inf\biggl\{\int_\Omega \lvert{D\phi}\rvert^pdx+\beta \int_{\partial^* \Omega}\lvert{\phi}\rvert^pd\mathcal{H}^{n-1},\; \phi \in W^{1,p}(\Omega),\;\phi…
Membranes are of great technological and biological as well as theoretical interest. Two main classes of membranes can be distinguished: Fluid membranes and polymerized, tethered membranes. Here, we review progress in the theoretical…
This paper addresses optimal design problems governed by multi-state stationary diffusion equations, aiming at the simultaneous optimization of the domain shape and the distribution of two isotropic materials in prescribed proportions.…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
In this paper, we study a maximization and a minimization problem associated with a Poisson boundary value problem. Optimal solutions in a set of rearrangements of a given function define stationary and stable flows of an ideal fluid in two…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
A geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements, and is suitable for both solid and liquid membranes. The curvilinear coordinate system is used to describe…