Related papers: Generating true minima in constrained variational …
We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the…
In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a…
In mechanics, common energy principles are based on fixed boundary conditions. However, in bridge engineering structures, it is usually necessary to adjust the boundary conditions to make the structure's internal force reasonable and save…
We formulate an optimization problem of Hamiltonian design based on the variational principle. Given a variational ansatz for a Hamiltonian we construct a loss function to be minimised as a weighted sum of relevant Hamiltonian properties…
In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a…
There exists in nature many examples of systems presenting self-limiting behaviour: population dynamics, structure engineering, Townsend's electron breakdown, nuclear decay in radioactive equilibrium, histeresis process, meteorological…
We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and…
Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the…
In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from…
The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…
In this paper, we consider numerical approximations for the optimal partition problem using Lagrange multipliers. By rewriting it into constrained gradient flows, three and four steps numerical schemes based on the Lagrange multiplier…
The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, {\it rotors}, and…
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
Constrained optimization problems exist in many domains of science, such as thermodynamics, mechanics, economics, etc. These problems are classically solved with the help of the Lagrange multipliers and the Lagrangian function. However, the…
Based on a characterization of the optimality of a feasible solution of a convex entropy minimization problem, one shows that the feasible solutions obtained using formally the Lagrange multipliers method are optimal.
We deliver a novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping by establishing a restricted Hamilton's principle. Fractional damping is a particular instance of non-local (in…