The size and complexity of modern astronomical surveys has grown to the point where, in many cases, traditional human scheduling of observations is tedious at best and impractical at worst. Automated scheduling algorithms present an opportunity to save human effort and increase scientific productivity. A common scheduling challenge involves determining the optimal ordering of a … Read more
This paper investigates the design and analysis of price formation in wholesale electricity markets given variability, uncertainty, non-convexity, and intertemporal operating constraints. The paper’s primary goal is to develop a framework to assess the many resource participation models, reserve product definitions, and enhanced pricing methods that have arisen in U.S. systems, especially in the context … Read more
Renewable Energy Communities (RECs) are an important building block for the decarbonization of the energy sector. The concept of RECs allows individual consumers to join together in local communities to generate, store, consume and sell renewable energy. A major benefit of this collective approach is a better match between supply and demand profiles, and thus, … Read more
Problem definition: We study the problem of designing large-scale resilient relay logistics hub networks. We propose a model of k-Shortest Path Network Design, which aims to improve a network’s efficiency and resilience through its topological configuration, by locating relay logistics hubs to connect each origin-destination pair with k paths of minimum lengths, weighted by their … Read more
The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. In recent years, data-driven scientific discovery has emerged as a viable competitor in … Read more
Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical … Read more
Stochastic Dual Dynamic Programming (SDDP) is a widely used and fundamental algorithm for solving multistage stochastic optimization problems. Although SDDP has been frequently applied to solve risk-averse models with the Conditional Value-at-Risk (CVaR), it is known that the estimation of upper bounds is a methodological challenge, and many methods are computationally intensive. In practice, this … Read more
This study presents a polynomial time algorithm to solve the lossless battery charging problem. In this problem the optimal charging and discharging schedules are chosen to maximize total profit. Traditional solution approaches have relied on either approximations or exponential algorithms. By studying the optimality conditions of this problem, we are able to reduce it to … Read more
\(\) We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems where convex optimization problems are built from sampled observations. We begin by introducing a set of condition numbers related to sharpness in \(\ell_p\) or Schatten-p norms (\(p\in[1,2]\)) based on nonsmooth reformulations of a class of convex optimization problems, including sparse recovery, … Read more
The pooling problem is a classical NP-hard problem in the chemical process and petroleum industries. This problem is modeled as a nonlinear, nonconvex network flow problem in which raw materials with different specifications are blended in some intermediate tanks, and mixed again to obtain the final products with desired specifications. The analysis of the pooling … Read more