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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…
The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle…
We consider the coupled problems of optimal thermostat programming and optimal pricing of electricity. Our framework consists of a single user and a single provider (a regulated utility). The provider sets prices for the user, who pays for…
We study the joint scheduling of behind-the-meter distributed energy resources (DERs), including flexible loads, renewable generation, and battery energy storage systems, under net energy metering tariffs with demand charges. The problem is…
A very simple example of an algorithmic problem solvable by dynamic programming is to maximize, over sets A in {1,2,...,n}, the objective function |A| - \sum_i \xi_i 1(i \in A,i+1 \in A) for given \xi_i > 0. This problem, with random…
Column generation and branch-and-price are leading methods for large-scale exact optimization. Column generation iterates between solving a master problem and a pricing problem. The master problem is a linear program, which can be solved…
Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
In this paper we formulate an optimization approach to schedule electrical loads given a short term prediction of time-varying power production and the ability to store only a limited amount of electrical energy. The proposed approach is…
A significant portion of a consumer's annual electrical costs can be made up of coincident peak charges: a transmission surcharge for power consumed when the entire system is at peak demand. This charge occurs only a few times annually, but…
We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following: we first find the contract that is optimal…
We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a dynamic programming formulation that is…
In this paper, we consider the problem of optimal demand response and energy storage management for a power consuming entity. The entity's objective is to find an optimal control policy for deciding how much load to consume, how much power…
Energy usage optimal scheduling has attracted great attention in the power system community, where various methodologies have been proposed. However, in real-world applications, the optimal scheduling problems require reliable energy…
In this paper we introduce the problem of dynamic pricing of power for smart-grid networks. This is studied within a network utility maximization (NUM) framework in a deterministic setting with a single provider, multiple users and a finite…
Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue.…
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…
Minimizing the peak power consumption and matching demand to supply, under fixed threshold polices, are two key requirements for the success of the future electricity market. In this work, we consider dynamic pricing methods to minimize the…
In this report, we provide a technical sequence on tackling the solar PV and demand forecast as well as optimal scheduling problem proposed by the IEEE-CIS 3rd technical challenge on predict + optimize for activity and battery scheduling.…
How to compute (super) hedging costs in rather general fi- nancial market models with transaction costs in discrete-time ? Despite the huge literature on this topic, most of results are characterizations of the super-hedging prices while it…