LAGRANGE
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Related Articles from SNS
Lagrange multipliers in Maximum likelihood estimations and Least squares problems with Constraints
Announce Type: cross Abstract: This study investigates a statistical property of Lagrange multipliers in constrained Maximum Likelihood Estimation (MLE) and Least Squares (LS) problems from the perspective of numerical optimization. Building on large-sample theory, we show that the associated Lagrange multipliers converge to zero as the sample size increases, provided the distribution is correctly specified in MLE or the residuals are normally distributed in LS. Although this asymptotic...
Physics-Aware Sparse Learning and Selective Online Adaptation for Euler-Lagrange Robot Dynamics
Announce Type: new Abstract: Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models...
Adaptive Artificial Time-Delay Control with Barrier Lyapunov Constraints for Euler-Lagrange Robots
Announce Type: new Abstract: This paper addresses the challenge of simultaneously compensating for state-dependent uncertainties and enforcing time-varying state constraints in Euler-Lagrange systems, a common requirement in robotics that remains underserved by existing control designs. A novel adaptive control framework is developed that combines an artificial time-delay-based uncertainty estimation strategy, also known as time-delay estimation, with a barrier Lyapunov function to enforce...
Variational Openness: An Open Formulation of Hamilton's Principle
arXiv:2606.08659v1 Announce Type: new Abstract: Since its classical origin, Hamilton's principle has been formulated under an exact closure condition: admissible variations vanish at the boundaries of the variational domain. This condition removes the boundary term in the first variation of the action and yields the Euler--Lagrange equation. Although natural for isolated deterministic systems, fixed boundary admissibility is usually treated as a technical condition rather than as a physical...
A variational formulation of the adjoint Kutta condition in potential flow
arXiv:2606.06937v1 Announce Type: new Abstract: We give a variational formulation of the continuous adjoint Kutta condition for two-dimensional subcritical potential flow, with emphasis on the Kutta condition and the role of the wake. We show that the adjoint Kutta condition can be imposed by a penalty term evaluated at the trailing edge, with the corresponding Lagrange multiplier determined by stationarity of the Lagrangian with respect to circulation, and that a wake treatment is not...
A Voxel-Based Quantum Computing Method (VBQC) for Solid Mechanics Problem
new Abstract: Quantum computing presents a promising method to overcome the efficiency and memory constraints in large-scale mechanical problems, with numerous successful applications demonstrated in fluid mechanics. However, solid mechanics problems usually require irregular grids for spatial discretization, due to the Lagrange formulations and complex boundaries, which makes the quantum simulation of the system matrix, e.g., the mass or stiffness matrix which is often referred to as the...
Modified augmented Lagrangian preconditioning for mixed-dimensional beam-solid coupling
Announce Type: new Abstract: This paper presents modified augmented Lagrangian block preconditioners for the mixed-dimensional coupling of three-dimensional solid bodies with embedded one-dimensional torsion-free Kirchhoff-Love beams using Lagrange multipliers for constraint enforcement. The finite element discretization of this mixed formulation leads to an indefinite saddle-point system. An augmented Lagrangian formulation is employed to regularize the linear system while maintaining exact...
Hessian-recovery-based C0 finite element methods for non-divergence form elliptic equations
arXiv:2606.03276v1 Announce Type: new Abstract: A Hessian-recovery-based C0 finite element framework is proposed for second-order elliptic equations in non-divergence form. The construction is based on a direct approximation of the strong non-divergence operator: the Hessian D2u is replaced by a recovered Hessian Hhuh, so that A : D2u is approximated by A : Hhuh. The resulting discretizations include a nodal formulation and a Galerkin-type formulation for general Lagrange finite element...
Functional Renormalization for Elastic Burgulence
Announce Type: new Abstract: We formulate elastic and elasto-inertial turbulence in the Martin-Siggia-Rose path-integral formalism and develop a systematic source-extended symmetry algorithm to derive Ward identities directly from the Euler-Lagrange equations. These identities provide nonperturbative constraints and a principled foundation for constructing closure schemes. As a dimensionally reduced model for elastic turbulence, we propose an extended Burgers equation that preserves the...
Augmented Lagrangian Predictive Coding
arXiv:2605.31022v1 Announce Type: new Abstract: Predictive coding (PC) is a local-learning alternative to backpropagation (BP), training deep networks via local energy-minimization dynamics rather than a global backward pass. We introduce Augmented Lagrangian Predictive Coding (PC-ALM), which maintains PC's inference budget but aligns each weight update toward BP by accumulating per-layer constraint errors into a layer-local Lagrange multiplier. In linear PC networks, PC-ALM converges to an...