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Traditional lens design is a numerical and forward process based on ray tracing and aberration theory. This method has limitations because the initial configuration of the lens has to be specified and the aberrations of the lenses have to…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
The Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method is a cutting-edge distributed optimization algorithm known for its superior numerical performance. It relies on each agent transmitting information to a central…
We propose a monotone, and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized Infinity Laplacian, which could be related to the family of so--called two--scale methods. We show that this method is…
The quadratic system provided by the Time of Arrival technique can be solved analytically or by optimization algorithms. In practice, a combination of both methods is used. An important problem in quadratic optimization is the possible…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was…
In this paper we comment the Post inversion formula for Laplace transform, and its possible application to the branch of Analytic Number theory (Arithmetical functions, RH and PNT), involving a condition in the form of iterated limit to…
In this paper, we develop rapidly convergent forward-backward algorithms for computing zeroes of the sum of finitely many maximally monotone operators. A modification of the classical forward-backward method for two general operators is…
Solving inverse problems by dynamical variant of the BC-method is basically reduced to inverting the connecting operator $C^T$ of the dynamical system, for which the problem is stated. Realizing the method numerically, one needs to invert…
In this paper, we obtain the analytical solutions of Laplace transforms based some novel integrals with suitable convergence conditions, by using hypergeometric approach (some algebraic properties of Pochhammer symbol and classical…
Recent advances in optimization theory have shown that smooth strongly convex finite sums can be minimized faster than by treating them as a black box "batch" problem. In this work we introduce a new method in this class with a theoretical…
We consider a linear inhomogeneous fractional evolution equation which is obtained from a Cauchy problem by replacing its first-order time derivative with Caputo's fractional derivative. The operator in the fractional evolution equation is…
The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
This article presents original work combining a NURBS-based inverse analysis with both kinematic and constitutive nonlinearities to recover the applied loads and deformations of thin shell structures. The inverse formulation is tackled by…
In the present paper authors introduce the L_n-integral transform and the inverse integral transform for n = 2^k, k=0,1,2,..., as a generalization of the classical Laplace transform and the inverse Laplace transform, respectively.…
Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with each other. For example, image super-resolution requires joint estimation of the image and motion…
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have…
Many research has been conducted about quadratic programming and inverse optimization. In this paper we present the combination aspect of these subjects, applying on transportation problem. First, we obtain the inverse form of quadratic…