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We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
We consider an impulse control problem in infinite horizon. To solve this problem, we extend to the infinite horizon case results of double barrier reflected backward stochastic differential equations. The properties of the Snell envelope…
Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method…
We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to…
A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
In the classical many normal means with different variances, we consider the situation when the observer is allowed to allocate the available measurement budget over the coordinates of the parameter of interest. The benchmark is the minimax…
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…
A memetic framework for optimal inverse design is proposed by combining a local gradient-based procedure and a robust global scheme. The procedure is based on method-of-moments matrices and does not demand full inversion of a system matrix.…
We consider the optimal multi-agent persistent monitoring problem defined by a team of cooperating agents visiting a set of nodes (targets) on a graph with the objective of minimizing a measure of overall node state uncertainty. The…
This paper describes the structure of optimal policies for discounted periodic-review single-commodity total-cost inventory control problems with fixed ordering costs for finite and infinite horizons. There are known conditions in the…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely…
We aim to generalize the results of Cai and Nitta (2007) by allowing both the utility and production function to depend on time. We also consider an additional intertemporal optimality criterion. We clarify the conditions under which the…
Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…
We prove a maximum principle for the problem of optimal control for a fractional diffusion with infinite horizon. Further, we show existence of fractional backward stochastic differential equations on infinite horizon. We illustrate our…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
We adopt an optimal-control framework for addressing the undiscounted infinite-horizon discrete-time restless $N$-armed bandit problem. Unlike most studies that rely on constructing policies based on the relaxed single-armed Markov Decision…
In this paper, we study the optimal stopping problem in the case where the reward is given by a family $(\phi(\tau ),\;\;\tau \in \stopo)$ of non negative random variables indexed by predictable stopping times. We treat the problem by means…
For nonexpansive fixed-point problems, Halpern's method with optimal parameters, its so-called H-dual algorithm, and in fact, an infinite family of algorithms containing them, all exhibit the exactly minimax optimal convergence rates. In…