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In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems, for which we have access to exact information of constraints and noisy function values of the objective. We propose a Bregman linearized augmented…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…
Long time-duration low-thrust nonlinear optimal spacecraft trajectory global search is a computationally and time expensive problem characterized by clustering patterns in locally optimal solutions. During preliminary mission design,…
We derive a variant of the nonsmooth maximum principle for problems with pure state constraints. The interest of our result resides on the nonsmoothness itself since, when applied to smooth problems, it coincides with known results.…
This paper deals with optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which…
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…
The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…
This paper presents a novel framework for the continuation method of model predictive control based on optimal control problem with a nonsmooth regularizer. Via the proximal operator, the first-order optimality inclusion relation is…
Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
Multi-revolution low-thrust trajectory optimization problems are important and challenging in space mission design. In this paper, an efficient, accurate, and widely applicable pseudospectral method is proposed to solve multi-revolution…
A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…
Nonsmooth sparsity constrained optimization encompasses a broad spectrum of applications in machine learning. This problem is generally non-convex and NP-hard. Existing solutions to this problem exhibit several notable limitations,…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett…