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In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the…
A Pontryagin maximum principle for an optimal control problem in three dimensional linearized compressible viscous flows is established using the Ekeland variational principle. The controls are distributed over a bounded domain, while the…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
We present a novel method called TESALOCS (TEnsor SAmpling and LOCal Search) for multidimensional optimization, combining the strengths of gradient-free discrete methods and gradient-based approaches. The discrete optimization in our method…
The manipulation of a collection of fluid particles in a low Reynolds number environment has several important applications. As we demonstrate in this paper, this manipulation problem is related to the scientific question of how fluid flow…
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
We derive novel, fast, and parameter-robust preconditioned iterative methods for steady and time-dependent Navier--Stokes control problems. Our approach may be applied to time-dependent problems which are discretized using backward Euler or…
The numerical solution of kinetic equations is challenging due to the high dimensionality of the underlying phase space. In this paper, we develop a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT)…
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…
Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose…
We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…
We study low-rank tensor methods for the numerical solution of Schr\"odinger's equation with time-independent and explicitly time-dependent Hamiltonians, motivated by large-scale simulations of many-body quantum systems and quantum…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…
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…
We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates…
The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…