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Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an It\^o type stochastic differential equation with control process entering both in the drift and the…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…
We provide theoretical foundations and computational tools for the systematic design of optimization-based control laws with constraints that have different priorities. By introducing the concept of prioritized intersections, we extend and…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an…
We present formulations and numerical algorithms for solving diffeomorphic shape matching problems. We formulate shape matching as a variational problem governed by a dynamical system that models the flow of diffeomorphism $f_t \in…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
Safety-critical cyber-physical systems require control strategies whose worst-case performance is robust against adversarial disturbances and modeling uncertainties. In this paper, we present a framework for approximate control and learning…
A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
We consider the uniform parallel machines scheduling problem in the context of optimistic bilevel optimization, where two speed options are considered. In this scenario, the leader aims to minimize the weighted number of tardy jobs, while…
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization…
We present a dynamic programming-based solution to a stochastic optimal control problem up to a hitting time for a discrete-time Markov control process. Firstly, we determine an optimal control policy to steer the process toward a compact…
An optimal control problem for the continuity equation is considered. The aim of a controller is to maximize the total mass within a target set at a given type moment. An iterative numerical algorithm for solving this problem is presented.
The problem of automatically clustering data is an age old problem. People have created numerous algorithms to tackle this problem. The execution time of any of this algorithm grows with the number of input points and the number of cluster…