Related papers: Adjoint System in the Shooting Method to Solve Bou…
The solving of scientific and practical application connected with conducting of satellite experiments and measurement demand analysis of geometric and physic conditions according to different kind of models. This is forced in connect of…
This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…
Generally, multi-objective optimisation problems are solved exactly or approximated by solving a series of scalarisations, for example by dichotomic search. In this paper, we take a different approach and attempt to compute the set of all…
In an earlier paper (https://doi.org/10.1137/21M1393315), the Switch Point Algorithm was developed for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
We formulate, in lattice-theoretic terms, two novel algorithms inspired by Bradley's property directed reachability algorithm. For finding safe invariants or counterexamples, the first algorithm exploits over-approximations of both forward…
We describe the shrinking target problem for random iterated function systems which semi-conjugate to a random subshifts of finite type. We get the Hausdorff dimension of the set based on shrinking target problems with given targets. The…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
This paper aims to solve the equations of geometrically exact 3D nonlinear Cosserat static rods under large displacements with a mesh free alternative method to finite elements: the shooting method. One of the main goal of the work…
Few-shot learning aims to transfer the knowledge acquired from training on a diverse set of tasks to unseen tasks from the same task distribution with a limited amount of labeled data. The underlying requirement for effective few-shot…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
We develop a general form of the Ritz method for trial functions that do not satisfy the essential boundary conditions. The idea is to treat the latter as variational constraints and remove them using the Lagrange multipliers. In…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
A tutorial is presented which demonstrates the theory and usage of the Parker-Sochacki method of numerically solving systems of differential equations. Solutions are demonstrated for the case of projectile motion in air, and for the…
In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Parametric optimal control problems governed by partial differential equations (PDEs) are widely found in scientific and engineering applications. Traditional grid-based numerical methods for such problems generally require repeated…