Related papers: Hamilton-Jacobi equations for finite-rank matrix i…
In this paper we present a mathematical and numerical analysis of an eigenvalue problem associated to the elasticity-Stokes equations stated in two and three dimensions. Both problems are related through the Herrmann pressure. Employing the…
Matrix rank and inertia optimization problems are a class of discontinuous optimization problems, in which the decision variables are matrices running over certain feasible matrix sets, while the ranks and inertias of the variable matrices…
We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly…
In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton--Jacobi theory for these systems following two approaches, obtaining two different…
Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure.…
In this work we obtain the planar free energy for the Hermitian one-matrix model with various choices of the potential. We accomplish this by applying an approach that bypasses the usual diagonalization of the matrices and the introduction…
Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled…
For higher derivative theories, using the approach of Caratheodory's equivalent Lagrangian, we show that there exist novel formulations of Hamilton-Jacobi equations, which are different from the formulations derived from Hamilton's…
In this paper, we derive the lower bounds for the gradients of viscosity solutions to the Hamilton--Jacobi equation, where the convex Hamiltonian depends on the unknown function. We obtain gradient estimates using two different methods.…
We study a one-parameter family of Eikonal Hamilton-Jacobi equations on an embedded network, and prove that there exists a unique critical value for which the corresponding equation admits global solutions, in a suitable viscosity sense.…
In this note, we discuss a class of time-dependent Hamilton-Jacobi equations depending on a function of time, this function being chosen in order to keep the maximum of the solution to the constant value 0. The main result of the note is…
On the grounds of a Feynman-Kac--type formula for Hamiltonian lattice systems we derive analytical expressions for the matrix elements of the evolution operator. These expressions are valid at long times when a central limit theorem…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
Many problems of theoretical and practical interest involve finding a convex or concave function. For instance, optimization problems such as finding the projection on the convex functions in $H^k(\Omega)$, or some problems in economics. In…
A new algorithm for time dependent Hamilton Jacobi equations on networks, based on semi Lagrangian scheme, is proposed. It is based on the definition of viscosity solution for this kind of problems recently given in. A thorough convergence…
Reduction theory has played a major role in the study of Hamiltonian systems. On the other hand, the Hamilton-Jacobi theory is one of the main tools to integrate the dynamics of certain Hamiltonian problems and a topic of research on its…
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…
We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power $\beta$ by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting…
A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…