The variability of wind and solar photovoltaic (PV) generation poses significant risks for producers in day-ahead electricity markets, where commitments must be made before actual output is realized. A common mitigation strategy is to invest in storage, but an alternative is to exploit the natural complementarity between wind and solar resources. We evaluate this economic … Read more
The decarbonization of short-haul air transport has gained increasing attention, with electric aircraft emerging as a promising alternative to conventional short-haul aviation. However, given the substantial investment anticipated for the necessary infrastructure, a strategic and globally coordinated selection of airports is imperative. The aim of this paper is to address this problem and determine the … Read more
Problem Definition: Final exam scheduling is a common but challenging optimization problem. At Bucknell University, a small liberal arts institution, the problem is particularly complex and has historically required the Registrar’s Office to spend months manually designing an exam schedule each semester. Methodology: We worked in close collaboration with the Registrar’s Office. First, we created … Read more
The primary challenges in systemic risk measurement involve determining an overall reserve level of risk capital and allocating it to different components based on their systemic relevance. In this paper, we introduce a multivariate loss ratio measure (MLRM), which is the minimum amount of capital to be injected into a financial system such that the … Read more
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In many derivative-free optimization algorithms, a sufficient decrease condition decides whether to accept a trial step in each iteration. This condition typically requires that the potential objective function value decrease of the trial step, i.e., the true reduction in the objective function value that would be achieved by moving from the current point to the … Read more
In this paper, we propose the Bregman Douglas-Rachford splitting (BDRS) method and its variant Bregman Peaceman-Rachford splitting method for solving maximal monotone inclusion problem. We show that BDRS is equivalent to a Bregman alternating direction method of multipliers (ADMM) when applied to the dual of the problem. A special case of the Bregman ADMM is … Read more
We show how to extract alternative solutions for optimization problems solved by Benders Decom- position. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative solutions but none appear to support such generation when using Benders Decomposition. We propose a new post-processing method that extracts multiple optimal and … Read more
Part I of this work [Gao25] establishes online scaled gradient methods (OSGM), a framework that utilizes online convex optimization to adapt stepsizes in gradient methods. This paper focuses on the practical aspects of OSGM. We leverage the OSGM framework to design new adaptive first-order methods and provide insights into their empirical behavior. The resulting method, … Read more
This work is concerned with the convergence rate analysis of the Dou- glas–Rachford splitting (DRS) method for finding a zero of the sum of two maximally monotone operators. We obtain an exact rate of convergence for the DRS algorithm and demonstrate its sharpness in the setting of convex feasibility problems. Further- more, we investigate the … Read more