Related papers: The Principle of Optimality in Dynamic Programming…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
We consider a Bolza-type optimal control problem for a dynamical system described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1)$. The value of this problem is introduced as a functional in a…
This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
This brief note considers the problem of learning with dynamic-optimizing principal-agent setting, in which the agents are allowed to have global perspectives about the learning process, i.e., the ability to view things according to their…
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…
When applying optimization method to a real-world problem, the possession of prior knowledge and preliminary analysis on the landscape of a global optimization problem can give us an insight into the complexity of the problem. This…
This paper explores the fundamental properties of distributed minimization of a sum of functions with each function only known to one node, and a pre-specified level of node knowledge and computational capacity. We define the optimization…
We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are…
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
We prove a maximality theorem for one-parameter dynamical systems including multiplier one-parameter dynamical systems. Our main result is new even for one-parameter actions on commutative multiplier algebras including the algebra of…
Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…
This paper presents an axiomatic approach to finite Markov decision processes where the discount rate is zero. One of the principal difficulties in the no discounting case is that, even if attention is restricted to stationary policies, a…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
Reinforcement learning based adaptive/approximate dynamic programming (ADP) is a powerful technique to determine an approximate optimal controller for a dynamical system. These methods bypass the need to analytically solve the nonlinear…
In this work we study the interplay between the dynamics of a model of diffusion governed by a mechanism of imitation and its underlying structure. The dynamics of the model can be quantified by a macroscopic observable which permits the…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…