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The Double Linear Policy (DLP) framework guarantees a Robust Positive Expectation (RPE) under optimized constant-weight designs or admissible prespecified time-varying policies. However, the sequential optimization of these time-varying…
This paper deals with the problem of clearing sequential electricity markets under uncertainty. We consider the European approach, where reserves are traded separately from energy to meet exogenous reserve requirements. Recently pro- posed…
Designing spacecraft trajectories remains challenging in the presence of stochastic effects such as maneuver execution errors and observation uncertainties. Although covariance control and belief-space planning provide useful tools for…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
This paper introduces a multi-timescale stochastic programming framework designed to address decision-making challenges in power systems, particularly those with high renewable energy penetration. The framework models interactions across…
In the optimization under uncertainty, decision-makers first select a wait-and-see policy before any realization of uncertainty and then place a here-and-now decision after the uncertainty has been observed. Two-stage stochastic programming…
We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one…
This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…
This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…
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…
In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical data and the information on the true utility function is incomplete. To mitigate…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
The multi-energy management framework of industrial parks advocates energy conversion and scheduling, which takes full advantage of the compensation and temporal availability of multiple energy. However, how to exploit elastic loads and…
This paper extends the single-item single-stocking location non-stationary stochastic inventory problem to relax the assumption of independent demand. We present a mathematical programming-based solution method that relaxes the assumption…
We consider a general class of Dynamic Programming (DP) problems with non-separable objective functions. We show that for any problem in this class, there exists an augmented-state DP problem which satisfies the Principle of Optimality and…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…
Data-Driven Predictive Control (DDPC) has been recently proposed as an effective alternative to traditional Model Predictive Control (MPC), in that the same constrained optimization problem can be addressed without the need to explicitly…
In this paper, we discuss an application of the SDDP type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse…
The type of decision dependent uncertainties (DDUs) imposes a great challenge in decision making, while existing methodologies are not sufficient to support many real practices. In this paper, we present a systematic study to handle this…