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Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However,…
In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
We present a new view onto the successive approximations' approach in study of the two-point nonlinear fractional boundary value problems. In order to reduce the original problem and further construct its approximate solution we use the…
For one class of boundary value problem depending on small parameter for which numerical methods for their solution are actually inapplicable, procedure of limiting problem acquisition which is much easier and which solution as much as…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
Optimizing shapes and topology of physical devices is crucial for both scientific and technological advancements, given its wide-ranging implications across numerous industries and research areas. Innovations in shape and topology…
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
In this paper, the author establishes the existence of positive entire solutions to a general class of semilinear poly-harmonic systems, which includes equations and systems of the weighted Hardy--Littlewood--Sobolev type. The novel method…
Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work…
In this paper we report and compare the numerical results for an ocean circulation model obtained by the classical truncated boundary formulation, the free boundary approach and a quasi-uniform grid treatment of the problem. We apply a…
We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…
Automated code generation allows for a separation between the development of a model, expressed via a domain specific language, and lower level implementation details. Algorithmic differentiation can be applied symbolically at the level of…
I development a Conjugate Gradient Method for solving a partial differential system with multiply controls. Some numerical results are depicted. Also, I present an explication of why the control over a partial differential equations system…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
A new numerical method for solving a scalar ordinary differential equation with a given initial condition is introduced. The method is using a numerical integration procedure for an equivalent integral equation and is called in this paper…
Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable…
This article presents an alternative approach to finite elements for modeling and analyzing 3D static mooring lines using string theory and the shooting method (SM) to solve two-point boundary value problems (TPBVPs) for 3D nonlinear static…
In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian…