Tootfinder

Primer to get you started with Optimization and Mathematical Programming in R #rstats

CRAN Task View: Optimization and Mathematical Programming
This CRAN Task View contains a list of packages that offer facilities for solving optimization problems. Although every regression model in statistics solves an optimization problem, they are not part of this view. If you are looking for regression methods, the following views will also contain useful starting points: MachineLearning, Econometrics, Robust Packages are categorized according to the following sections. See also the “Related Links” and “Other Resources” sections at the end.

A Concept for Autonomous Problem-Solving in Intralogistics Scenarios
Johannes Sigel, Daniel Dittler, Nasser Jazdi, Michael Weyrich
https://arxiv.org/abs/2507.03534

A Concept for Autonomous Problem-Solving in Intralogistics Scenarios
Achieving greater autonomy in automation systems is crucial for handling unforeseen situations effectively. However, this remains challenging due to technological limitations and the complexity of real-world environments. This paper examines the need for increased autonomy, defines the problem, and outlines key enabling technologies. A structured concept is proposed, consisting of three main steps: context enrichment, situation analysis, and generation of solution strategies. By following this …

Computing $H$-equations with 2-by-2 integral matrices
Gemma Bastardas, Enric Ventura
https://arxiv.org/abs/2506.05272 https://arxiv.o…

Computing $H$-equations with 2-by-2 integral matrices
We study the transference through finite index extensions of the notion of equational coherence, as well as its effective counterpart. We deduce an explicit algorithm for solving the following algorithmic problem about size two integral invertible matrices: ''given $h_1,\ldots, h_r; g\in \operatorname{PSL}_2(\mathbb{Z})$, decide whether $g$ is algebraic over the subgroup $H=\langle h_1,\ldots ,h_r\rangle \leqslant \operatorname{PSL}_2(\mathbb{Z})$ (i.e., whether there exist a non-trivial $H$-eq…

Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games
Heidi Wolles Lj\'osheim, Dante Kalise, John W. Pearson, Francisco J. Silva
https://arxiv.org/abs/2507.01958

Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games
We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference discretization and solve the resulting finite-dimensional optimization problem using the Chambolle--Pock primal--dual algorithm. As this involves computing proximal operators and solving ill-conditioned linear systems at each iteration, we propose a general class of par…

"I forgot the formula:" How students can use coherence to reconstruct a (partially) forgotten equation
Katherine Gifford, Gabriel S. Ehrlich, Engin Bumbacher, Eric Kuo
https://arxiv.org/abs/2506.19641

"I forgot the formula:" How students can use coherence to reconstruct a (partially) forgotten equation
Introductory physics instruction emphasizes fluency with routine problem-solving procedures. However, even when applying these procedures, students frequently encounter challenges. This paper investigates how students navigate such moments when answering qualitative E&M problems in interviews. Students frequently noted they had partially forgotten a key equation on a problem involving RC circuits. We present focal cases that show how coherence-seeking approaches were employed to overcome this p…

Cluster Expansion Toward Nonlinear Modeling and Classification
Adrian Stroth, Claudia Draxl, Santiago Rigamonti
https://arxiv.org/abs/2506.18695 https://…

Cluster Expansion Toward Nonlinear Modeling and Classification
A quantitative first-principles description of complex substitutional materials like alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum-mechanical problem. Therefore, materials properties must be modeled. The Cluster Expansion (CE) method is widely used for this purpose, but it struggles with properties that exhibit non-linear dependencies on composition, often failing even in a qualitative description. By looking at CE through …

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
Gabriela Abadia-Doyle, William W. Hager, Anil V. Rao
https://arxiv.org/abs/2506.13938

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential equations and leads to the following important outcomes. First, the first-order optimality conditions of the LGL integral form are derived, which lead to a full-rank transformed adjoint system and novel costate estimate. Next, a derivative-like form of the LG…

Newton optimization for the Multiconfiguration Self Consistent Field method at the basis set limit: closed-shell two-electron systems
Evgueni Dinvay, Rasmus Vikhamar-Sandberg, Luca Frediani
https://arxiv.org/abs/2506.12906

Newton optimization for the Multiconfiguration Self Consistent Field method at the basis set limit: closed-shell two-electron systems
The multiconfiguration self-consistent-field (MCSCF) method is revisited with the specific focus on the two electron systems for simplicity. A wave function is represented as a linear combination of Slater determinants. Both orbitals and coefficients of this configuration interaction expansion are optimized following the variational principle making use of the Newton optimization technique. It reduces the MCSCF problem to solving a particular differential Newton system, which can be discretized…

Local feature filtering for scalable and well-conditioned Random Feature Methods
Jan Willem van Beek, Victorita Dolean, Ben Moseley
https://arxiv.org/abs/2506.17626

Local feature filtering for scalable and well-conditioned Random Feature Methods
In recent years, machine learning has emerged as a powerful tool for solving partial differential equations (PDEs), with randomized neural networks showing remarkable potential. These networks, typically shallow, differ from conventional approaches by randomizing all parameters except those in the final layer. Notably, by integrating techniques inspired by domain decomposition, they achieve improved local accuracy and computational efficiency. Following \cite{chen:2022:BTM}, we refer to these a…