Related papers: Performance Bounds for PDE-Constrained Optimizatio…
We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-dimensional random parameters. To address the critical…
We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the…
We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…
Constrained optimization offers a powerful framework to prescribe desired behaviors in neural network models. Typically, constrained problems are solved via their min-max Lagrangian formulations, which exhibit unstable oscillatory dynamics…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
We derive error estimates for a linear-quadratic elliptic distributed optimal control problem with pointwise control constraints that can be applied to standard finite element methods and multiscale finite element methods.
Approximate methods to solve stochastic optimal control (SOC) problems have received significant interest from researchers in the past decade. Probabilistic inference approaches to SOC have been developed to solve nonlinear quadratic…
This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances, and in presence of some amplitude constraints on the control…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form, and show error estimates and a convergence result of the value in some weak sense…
This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…
In this paper, we propose a class of discrete-time approximation schemes for stochastic optimal control problems under the $G$-expectation framework. The proposed schemes are constructed recursively based on piecewise constant policy. We…
The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
We study revenue maximization in a buyer-seller setting where the seller has a single object and the buyer has both a private valuation and a private budget. Private budgets complicate the classic single-product monopoly problem, making…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…