Related papers: A Primal-dual hybrid gradient method for solving o…
This paper introduces a new type of second order stochastic backward Hamilton-Jacobi-Bellman (HJB) equations for optimal stochastic control problems with a currently observable but non-predicable parameter process, in addition to the…
We propose novel connections between several neural network architectures and viscosity solutions of some Hamilton--Jacobi (HJ) partial differential equations (PDEs) whose Hamiltonian is convex and only depends on the spatial gradient of…
The optimal \(H_{\infty}\) control problem over an infinite time horizon, which incorporates a performance function with a discount factor \(e^{-\alpha t}\) (\(\alpha > 0\)), is important in various fields. Solving this optimal…
In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…
Many real-world control problems involve both discrete decision variables - such as the choice of control modes, gear switching or digital outputs - as well as continuous decision variables - such as velocity setpoints, control gains or…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associated fundamental equations such as the Bellman equation and the…
In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify…
In this work we propose a new primal-dual algorithm with adaptive step-sizes. The stochastic primal-dual hybrid gradient (SPDHG) algorithm with constant step-sizes has become widely applied in large-scale convex optimization across many…
We study a family of stationary Hamilton-Jacobi-Bellman (HJB) equations in Hilbert spaces arising from stochastic optimal control problems. The main difficulties to treat such problems are: the lack of smoothing properties of the linear…
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 address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically,…
We propose an approach for the synthesis of robust and optimal feedback controllers for nonlinear PDEs. Our approach considers the approximation of infinite-dimensional control systems by a pseudospectral collocation method, leading to…
We develop primal-dual coordinate methods for solving bilinear saddle-point problems of the form $\min_{x \in \mathcal{X}} \max_{y\in\mathcal{Y}} y^\top A x$ which contain linear programming, classification, and regression as special cases.…
We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the…