Related papers: Solving Linear Equations Over Maxmin-$\omega$ Syst…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
A novel approach is introduced for deriving exact solutions to nonlinear systems of ordinary differential equations. This method consists of four parts. In the initial part, the examined nonlinear differential equation system is transformed…
Matrix equations are omnipresent in (numerical) linear algebra and systems theory. Especially in model order reduction (MOR) they play a key role in many balancing based reduction methods for linear dynamical systems. When these systems…
We consider a class of production-inventory problems with box uncertainty sets from the seminal work of Ben-Tal et al. (2004) on linear decision rules in robust optimization. We prove that there always exists an optimal linear decision rule…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
The main aim of this paper is to study the growth of solutions of higher order linear differential equations using the concepts of $(\alpha ,\beta ,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-type. We obtain some results which improve…
This study addresses some algorithms for solving structured unconstrained convex optimiza- tion problems using first-order information where the underlying function includes high-dimensional data. The primary aim is to develop an…
Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…
In the parameterized problem \textsc{MaxLin2-AA}[$k$], we are given a system with variables $x_1,...,x_n$ consisting of equations of the form $\prod_{i \in I}x_i = b$, where $x_i,b \in \{-1, 1\}$ and $I\subseteq [n],$ each equation has a…
An iterative scheme for the Dynamical Systems Method (DSM) is given such that one does not have to solve the Cauchy problem occuring in the application of the DSM for solving ill-conditioned linear algebraic systems. The novelty of the…
A new approach for trajectory optimization of musculoskeletal dynamic models is introduced. The model combines rigid body and muscle dynamics described with a Hill-type model driven by neural control inputs. The objective is to find input…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
We propose a calculus for modeling implicit programming that supports first-class, overlapping, locally scoped, and higher-order instances with higher-kinded types. We propose a straightforward generalization of the well-established System…
We consider the harmonic balance method for finding approximate periodic solutions of the Lorenz system. When developing software that implements the described method, the math package Maxima was chosen. The drawbacks of symbolic…
In this work we present a power series method for solving ordinary and partial differential equations. To demonstrate our method we solve a system of ordinary differential equations describing the movement of a random walker on a…
The purpose of this work is to introduce a new idea of how to avoid the factorization of large matrices during the solution of stiff systems of ODEs. Starting from the general form of an explicit linear multistep method we suggest to…
We propose a study of structured non-convex non-concave min-max problems which goes beyond standard first-order approaches. Inspired by the tight understanding established in recent works [Adil et al., 2022, Lin and Jordan, 2022b], we…
A review of the authors's results is given. Several methods are discussed for solving nonlinear equations $F(u)=f$, where $F$ is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy…
This present paper provides the absolutely necessary corrections to the previous work entitled {\it A polynomial Time Algorithm to Solve The Max-atom Problem} (arXiv:2106.08854v1). The max-atom-problem (MAP) deals with system of scalar…