Related papers: A Data-embedded Solution Paradigm for Nonconvex Pr…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
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…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic…
This paper studies a structured compound stochastic program (SP) involving multiple expectations coupled by nonconvex and nonsmooth functions. We present a successive convex-programming based sampling algorithm and establish its…
The mathematical program with equilibrium constraints (MPEC) is a powerful yet challenging class of constrained optimization problems, where the constraints are characterized by a parametrized variational inequality (VI) problem. While…
Prediction deviations of different uncertainties have varying impacts on downstream decision-making. Improving the prediction accuracy of critical uncertainties with significant impacts on decision-making quality yields better optimization…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
Consensus-based optimization (CBO) is an agent-based derivative-free method for non-smooth global optimization that has been introduced in 2017, leveraging a surprising interplay between stochastic exploration and Laplace principle. In…
Within the realm of industrial technology, optimization methods play a pivotal role and are extensively applied across various sectors, including transportation engineering, robotics, and machine learning. With the surge in data volumes,…
This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given a first-order method, a function class, and a noise model…
We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and…
There have been recent efforts that combine seemingly disparate methods, extremum seeking (ES) optimization and partial differential equation (PDE) backstepping, to address the problem of model-free optimization with PDE actuator dynamics.…
The growing uncertainty from renewable power and electricity demand brings significant challenges to unit commitment (UC). While various advanced forecasting and optimization methods have been developed to predict better and address this…