Related papers: Monotone iterations of two obstacle problems with …
In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…
This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is…
In this note, we give a brief overview of obstacle problems for nonlocal operators, focusing on the applications to financial mathematics. The class of nonlocal operators that we consider can be viewed as infinitesimal generators of…
We describe several features of parallel or distributed asynchronous iterative algorithms such as unbounded delays, possible out of order messages or flexible communication. We concentrate on the concept of macroiteration sequence which was…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
The problem of implementing a class of functions with particular conditions by using monotonic multilayer functions is considered. A genetic algorithm is used to create monotonic functions of a certain class, and these are implemented with…
Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is…
We study an inverse drift problem for a two-dimensional parabolic equation on the unit square with mixed boundary conditions, where the drift coefficient is recovered from terminal observation data $g=u(\cdot,T)$. A monotone operator is…
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…
An iterative scheme for solving ill-posed nonlinear equations with locally $\sigma$-inverse monotone operators is studied in this paper. A stopping rule of discrepancy type is proposed. The existence of $u_{n_\delta}$ satisfying the…