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The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
In this paper, a spectral method based on conformal mappings is proposed to solve Steklov eigenvalue problems and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We build a new mathematical model of shape optimization for maximizing ionic concentration governed by the multi-physical coupling steady-state Poisson-Nernst-Planck system. Shape sensitivity analysis is performed to obtain the Eulerian…
The existence of global attractors is investigated for the Signorini problem with pointwise dissipation. It is shown that both the semilinear Signorini problem and the elastic obstacle problem with normal compliance exhibit exponential…
In this paper, we present passivity based convergence analysis of continuous time primal-dual gradient method for convex optimization problems. We first show that a convex optimization problem with only affine equality constraints admit a…
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…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
We introduce a model of infinite horizon linear dynamic optimization with linear constraints and obtain results concerning feasibility of trajectories and optimal solutions necessarily satisfying conditions that resemble the Euler condition…
Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality…
In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem, which acts as a framework for approximating the degenerate…
We consider general shape optimization problems governed by Dirichlet boundary value problems. The proposed approach may be extended to other boundary conditions as well. It is based on a recent representation result for implicitly defined…
The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is formulated by introducing a tracking-type cost functional…
We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…