We consider nonlinear heat conduction satisfying a variational principle of Fermat type in the case of stationary heat ̄ow. We review origins of a physical theory and transform it into a formalism consistent with irreversible thermodynamics, where the theory emerges as a consequence of the theorem of minimum entropy production. Applications of functional equations and the Hamilton±Bellman±Jacob...

This paper considers a class of optimization problems arising in wireless communication systems. We analyze the optimal control and the associated Hamilton–Jacobi–Bellman (HJB) equations. It turns out that the value function is a unique viscosity solution of the HJB equation in a certain function class. To deal with the fast growth condition of the value function in establishing uniqueness, we ...

We consider the optimal portfolio problem of a power investor who wishes to allocate her wealth between several credit default swaps (CDSs), a stock index, and a money market account. We model contagion risk among the reference entities in the portfolio using a reduced form Markovian model with interacting default intensities. Using the dynamic programming principle, we establish a lattice depe...

Abstract. This paper studies the bioremediation, in minimal time, of a water resource or reservoir using a single continuous bioreactor. The bioreactor is connected to two pumps, at different locations in the reservoir, that pump polluted water and inject back sufficiently clean water with the same flow rate. This leads to a minimal-time optimal control problem where the control variables are r...

We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field interaction under common noise. Our first main result is to state a dynamic programming principle for the value function in the Wasserstein space of probability measu...

The current work presents a deterministic asymptotically optimal feedback motion planning algorithm. Our algorithm is based on two well-established numerical practices: 1) the Fast Marching Method (FMM), which is a numerical solver for Hamilton-Jacobi-Bellman optimality equations, and 2) the adaptive mesh refinement algorithm designed to improve the resolution a simplicial mesh and the quality ...

RICHARD BELLMAN

In this paper, the optimal investment problem for an agent with dual risk model is studied. The financial market is assumed to be a diffusion process with the coefficients modulated by an external process, which is specified by the solution to a kind of stochastic differential equation. The object of the agent is to maximize the expected utility from terminal wealth. Together with the regularit...

The theory of control analyzes the proprieties of commanded systems. Problems of optimal control OC have been intensively investigated in the world literature for over forty years. During this period, series of fundamental results have been obtained, among which should be noted the maximum principle Pontryagin et al., 1962 and dynamic programming Bellman, 1963 . For many of the problems of the ...

We show that the stochastic Schrödinger equation for the filtered state of a system, with linear free dynamics, undergoing continual nondemolition measurement or either position or momentum, or both together, can be solved explicitly within a class of Gaussian states which we call extended coherent states. The asymptotic limit yields a class of relaxed states which we describe explicitly. Bellm...