相关论文: Convergence of dynamic programming principles for …
We consider the 0-1 Penalized Knapsack Problem (PKP). Each item has a profit, a weight and a penalty and the goal is to maximize the sum of the profits minus the greatest penalty value of the items included in a solution. We propose an…
In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…
This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…
We establish the existence and uniqueness of the solution to the Dirichlet problem for the variable exponent $p$-Laplacian on a bounded, smooth domain $\Omega \subset {\mathbb R}^n$, where the boundary datum belongs to $W^{1,p}(\Omega)$.…
In this paper, we consider a deterministic dynamic programming model, and derive the envelope theorem using the Clarke differential. Compared with previous research, we do not require differentiability, convexity, or boundedness.
We obtain the dynamic programming equations and optimality conditions akin to Pontryagin's extremum principle for certain mathematical models of hybrid control systems.
We construct some intrinsically defined discrete model of the magnetic Laplacian. The existence and uniqueness of solutions of the Dirichlet problem for the difference Poisson type equation are proved. We study in detail properties of the…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Dynamic optimization problems involving discrete decisions have several applications, yet lead to challenging optimization problems that must be addressed efficiently. Combining discrete variables with potentially nonlinear constraints…
Unique continuation principles are fundamental properties of elliptic partial differential equations, giving conditions that guarantee that the solution to an elliptic equation must be uniformly zero. Since finite-element discretizations…
In this paper, we investigate the monotonicity of solutions for a nonlinear equations involving the fractional Laplacian with variable exponent. We first prove different maximum principles involving this operator. Then we employ the direct…
This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show…
In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…