Related papers: An iterative Bregman regularization method for opt…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for…
This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…
In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic…
We study the Bregman Augmented Lagrangian method (BALM) for solving convex problems with linear constraints. For classical Augmented Lagrangian method, the convergence rate and its relation with the proximal point method is well-understood.…
The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in inverse problems and image processing based on Bregman…
All imaging modalities such as computed tomography (CT), emission tomography and magnetic resonance imaging (MRI) require a reconstruction approach to produce an image. A common image processing task for applications that utilise those…
Sparse training reduces the memory and computational costs of deep neural networks. However, sparse optimization methods, e.g., those adding an $\ell_1$ penalty, often control sparsity only indirectly through a regularization parameter…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
Optimal control of bilinear systems has been a well-studied subject in the areas of mathematical and computational optimal control. However, effective methods for solving emerging optimal control problems involving an ensemble of…
Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers…
We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
Many robotic sensor estimation problems can characterized in terms of nonlinear measurement systems. These systems are contaminated with noise and may be underdetermined from a single observation. In order to get reliable estimation…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…