Related papers: Generating true minima in constrained variational …
Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the principle of Least Action, the principle of Minimum Entropy Generation, and the Variational…
We present a practical numerical method for evaluating the Lagrange multipliers necessary for maintaining a constrained linear geometry of particles in dynamical simulations. The method involves no iterations, and is limited in accuracy…
Analyzing one example of LC circuit in [8], show its Lagrange problem only have other type critical points except for minimum type and maximum type under many circumstances. One novel variational principle is established instead of…
Because of the finiteness of the life span and boundedness of the physical space, the more reasonable or physical choice is the tempered power-law instead of pure power-law for the CTRW model in characterizing the waiting time and jump…
A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed…
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional.…
We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
The goal of this paper is to develop energy-preserving variational integrators for time-dependent mechanical systems with forcing. We first present the Lagrange-d'Alembert principle in the extended Lagrangian mechanics framework and derive…
We construct variations for the classes of regular solutions to degenerate Beltrami equations with restrictions of the set-theoretic type for the complex coefficient. On this basis, we prove the variational maximum principle and other…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
The paper concerns the study of criticality of Lagrange multipliers in variational systems that has been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments…
We formulate a finite-size particle numerical model of strongly magnetized plasmas in the drift-kinetic approximation. We use the phase space action as an alternative to previous variational formulations based on Low's Lagrangian or on a…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…