arXiv research

Study variational properties of curves in half-plane with area constraints.

New method for variational inference without conjugacy constraints.

New framework improves generative models with prediction and consistency constraints.

A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.

Improved Bayesian learning rule handles positive-definite constraints efficiently.

The paper studies stability of discrete planar curves using variational methods.

This work interprets SFA through variational inference, relaxing linearity constraints.

In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstraine…

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the geometrical setting. The constrained Euler-Lagrange equations are derived for ana…

Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing constraints on covariance, one can ensure consistency of linear response with the var…

Alternative discrete Dirac mechanics using Dirac structures.

New algorithm reduces regret and constraint violation in online convex optimization with complex constraints.

Discrete Lagrange problems solved with Lie group constraints.

Study optimal consumption with drawdown limits over a fixed time frame.

Paper presents a method to solve variational inequalities with general constraints without requiring analytic solutions.

Study optimizes perimeter in convex domains with anisotropic constraints.

New method for sampling on constrained domains using orthogonal-space gradient flow.

In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to constraints, optimal control theory and so on. This generalized variational calculu…

Generalizes Hamiltonian theory for variational problems, applied to first order gravity.

We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, i…

Abstract Morse index theorem applied to various optimization problems.

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constr…

New mass inequalities and proofs for causal variational principles.

The mathematical problem concerning intrinsic storage optimisation is formulated and solved by means of variational analysis. The solution, though obtained in implicit form, still sheds light on many important features of the optimal exercise strategy. It is shown how the solution depends on different constraint types …

New algorithm reduces dynamic regret for noisy gradient feedback with piecewise polynomial comparators.

Develops a first-order interior-point method for solving constrained variational inequalities.

This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror des…

Model predicts stable molecules with AI and physics constraints.

Study hypothesis testing under quantized samples with communication constraints, achieving near-optimal sample complexity.

We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an $L_{p,q}$-variation functional to quantify the change, which yields less variation for dynamic function sequences whose changes are constrai…

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and …

A novel approach for safe offline RL using latent safety constraints.

FairTrade uses variational inference to create fair predictions in causal models.

New model for shape graph registration with partial matching constraints.

VFlow enhances generative flows by augmenting data dimensions for better expressiveness.

Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $W=\int H^2$ under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the crit…

This paper proposes robust matrix variate regression models with rank constraints and vector regularization.

We derive a new model for pre-strained thin films, which consists of minimizing a biharmonic energy of deformations $v\in W^{2,2}$ satisfying the Monge-Ampère constraint $\det\nabla^2v = f$. We further discuss multiplicity properties of the minimizers of this model, in some special cases.

We develop a framework for incorporating structured graphical models in the \emph{encoders} of variational autoencoders (VAEs) that allows us to induce interpretable representations through approximate variational inference. This allows us to both perform reasoning (e.g. classification) under the structural constraints…

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Sev…

Framework for designing nonlinearities in neural networks with slope constraints.

New control theory for self-path-dependent problems solves unique constraints.

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulatio…

Extends Dirac structures to infinite dimensions for mechanical systems.

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In addition, for the problem to be a well-defined convex program, we must retain the conve…

Paper introduces CageBO for optimizing complex public policy problems.

PhysVarMix predicts diverse urban trajectories with physics constraints.

Optimal transport with path constraints for distributions of different masses.