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Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the…
We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
Predictive control is frequently used for control problems involving constraints. Being an optimization based technique utilizing a user specified so-called stage cost, performance properties, i.e., bounds on the infinite horizon…
This paper addresses the challenges of embedding common droop control characteristics in ac-dc power system steady-state simulation and optimization problems. We propose a smooth approximation methodology to construct differentiable…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…
We are interested in optimally controlling a discrete time dynamical system that can be influenced by exogenous uncertainties. This is generally called a Stochas-tic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle…
We consider the dynamic inventory problem with non-stationary demands. It has long been known that non-stationary (s, S) policies are optimal for this problem. However, finding optimal policy parameters remains a computational challenge as…
This paper provides a systematic comparison between Fitted Dynamic Programming (DP), where demand is estimated from data, and Reinforcement Learning (RL) methods in finite-horizon dynamic pricing problems. We analyze their performance…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct…
Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we…
This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the…
We consider a general aggregation framework for discounted finite-state infinite horizon dynamic programming (DP) problems. It defines an aggregate problem whose optimal cost function can be obtained off-line by exact DP and then used as a…
In this paper we discuss $\l$-policy iteration, a method for exact and approximate dynamic programming. It is intermediate between the classical value iteration (VI) and policy iteration (PI) methods, and it is closely related to optimistic…
We study the consistency of stochastic dynamic programs under converging probability distributions and other approximations. Utilizing results on the epi-convergence of expectation functions with varying measures and integrands, and the…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…