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We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
An optimal control problem with an infinite horizon quadratic cost functional for a linear system with a known additive disturbance is considered. The feature of this problem is that a weight matrix of the control cost in the cost…
It is known that the gradient method can be viewed as a dynamic system where various iterative schemes can be designed as a part of the closed loop system with desirable properties. In this paper, the finite-time and fixed-time convergence…
We prove three related quantitative results for the relative isoperimetric problem outside a convex body $\Omega$ in the plane: (1) {\L}ojasiewicz estimates and quantitative rigidity for critical points, (2) rates of convergence for the…
We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
This paper studies a finite horizon utility maximization problem on excessive consumption under a drawdown constraint. Our control problem is an extension of the one considered in Bahman et al. (2019) to the model with a finite horizon and…
We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a…
In this work, we introduce and study the controllability of the trajectories of a linear dynamical system, which can be used to solve the minimization of a quadratic function in finite dimension. We named this dynamical system the…
Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…
We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation…
Nonsmooth nonconvex optimization problems broadly emerge in machine learning and business decision making, whereas two core challenges impede the development of efficient solution methods with finite-time convergence guarantee: the lack of…
We consider a class of exit time stochastic control problems for diffusion processes with discounted criterion, where the controller can utilize a given amount of resource, called "fuel". In contrast to the vast majority of existing…
We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that…
This paper studies a variant of the minimum-cost flow problem in a graph with convex cost function where the demands at the vertices are functions depending on a one-dimensional parameter $\lambda$. We devise two algorithmic approaches for…
For a control system two major issues can be considered: the stabilizability with respect to a given target, and the minimization of an integral functional (while the trajectories reach this target). Here we consider a problem where…
We are interested in the gradient flow of a general first order convex functional with respect to the $L^1$-topology. By means of an implicit minimization scheme, we show existence of a global limit solution, which satisfies an…
In this paper, we consider the optimal control problem in a 3D flow model for incompressible rigid-viscoplastic media of the Bingham kind with homogeneous Dirichlet boundary conditions and a given cost functional. On the basis of methods of…