Related papers: Numerical Discretization Methods for the Discounte…
We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…
The derivation of second-order ordinary differential equations (ODEs) as continuous-time limits of optimization algorithms has been shown to be an effective tool for the analysis of these algorithms. Additionally, discretizing…
We study a signature-driven numerical scheme to solve multi-dimensional linear-quadratic (LQ) stochastic control problems. Using that linear signature functionals are dense in the natural class of admissible controls, we show that our…
We consider an optimal control problem governed by a one-dimensional elliptic equation that involves univariate functions of bounded variation as controls. For the discretization of the state equation we use linear finite elements and for…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively…
This paper studies the stochastic optimal control problem for systems with unknown dynamics. A novel decoupled data based control (D2C) approach is proposed, which solves the problem in a decoupled "open loop-closed loop" fashion that is…
The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
We compare the discretize-optimize (Disc-Opt) and optimize-discretize (Opt-Disc) approaches for time-series regression and continuous normalizing flows (CNFs) using neural ODEs. Neural ODEs are ordinary differential equations (ODEs) with…
We study a discrete-time random feature method for nonlinear, time-dependent partial differential equations. In contrast to continuous-time formulations that treat time as an additional input variable, the method advances the solution step…
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…
In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting…
We analyze a sequential quadratic programming algorithm for solving a class of abstract optimization problems. Assuming that the initial point is in an $L^2$ neighborhood of a local solution that satisfies no-gap second-order sufficient…
A discrete-time method for solving problems in optimal quantum control is presented. Controlling the time discretized markovian dynamics of a quantum system can be reduced to a Markov-decision process. We demonstrate this method in this…
We introduce a new algorithm for solving unconstrained discrete-time optimal control problems. Our method follows a direct multiple shooting approach, and consists of applying the SQP method together with an $\ell_2$ augmented Lagrangian…
This paper is concerned with a linear quadratic optimal control problem of delayed backward stochastic differential equations. An explicit representation is derived for the optimal control, which is a linear feedback of the entire past…
We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization…
This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programming (PQP) through dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data…
A discrete-time stochastic LQ problem with multiplicative noises and state transmission delay is studied in this paper, which does not require any definiteness constraint on the cost weighting matrices. From some abstract representations of…