Related papers: Time-dependent Generalized SIC-OEP formalism and G…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
Successive Interference Cancellation (SIC) is a powerful technique for managing interference in wireless networks, yet its optimal deployment in decentralized environments remains a challenge. This study investigates joint power and rate…
The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the…
A typical manipulation task consists of a manipulator equipped with a gripper to grasp and move an object with constraints on the motion of the hand-held object, which may be due to the nature of the task itself or from object-environment…
The 2-opt heuristic is a very simple local search heuristic for the traveling salesperson problem. In practice it usually converges quickly to solutions within a few percentages of optimality. In contrast to this, its running-time is…
Time-Optimal Path Parameterization (TOPP) is a well-studied problem in robotics and has a wide range of applications. There are two main families of methods to address TOPP: Numerical Integration (NI) and Convex Optimization (CO). NI-based…
This paper proposes a novel second-order optimization algorithm based on the Optimal Control Principle (OCP), applicable to large-scale optimization problems in neural network training. The algorithm has a computational complexity of O(d)…
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…
In this paper, we propose a parallel optimization method for electronic structure calculations based on a single orbital-updating approximation. It is shown by our numerical experiments that the method is efficient and reliable for atomic…
Optimizing high-level mission planning constraints is traditionally solved in exponential time and requires to split the problem into several ones, making the connections between them a convoluted task. This paper aims at generalizing…
Five time-dependent orbital optimized coupled-cluster (TD-ooCC) methods, of which four can converge to the complete active space self-consistent-field method, are presented for fermion-mixtures with arbitrary fermion kinds and numbers.…
In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for such problems, we introduce and analyze a new relaxed and…
A resolution complete optimal kinodynamic motion planning algorithm is presented and described as a generalized label correcting (GLC) method. In contrast to related algorithms, the GLC method does not require a local planning subroutine…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
Fermi-L\"owdin orbital self-interaction-correction (FLOSIC) method uses symmetric orthogonalized Fermi orbitals as localized orbitals in one-electron SIC schemes. In FLOSIC, a set of Fermi orbital descriptors (FOD) that define the FLOs is…
We propose a practical approximation to the exchange-correlation functional of (time-dependent) density functional theory for many-electron systems coupled to photons. The (time non-local) optimized effective potential (OEP) equation for…
We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual…
We present an atomic orbital based approximate scheme for self-interaction correction (SIC) to the local density approximation of density functional theory. The method, based on the idea of Filippetti and Spaldin [Phys. Rev. B 67, 125109…
Transformer-based self-attention mechanism serves as the core of modern language models, yet it often suffers from localization, where attentions collapse onto a limited subset of tokens and fail to capture long-range dependencies. To…
We calculate the electronic structure of several atoms and small molecules by direct minimization of the Self-Interaction Corrected Local Density Approximation (SIC-LDA) functional. To do this we first derive an expression for the gradient…