Linear Optimization: Theory and Applications

数据驱动的分析方法目前在许多行业中处于高效决策和决策支持的前沿。这种最先进的优化工具取得进展的一个突出例子是优化能源生产、储存、传输和交付以及交易。这些应用程序从操作时间范围扩展到战略时间范围。仅举几例，优化与机器学习等其他方法相结合，成功地改善了采油中的蒸汽辅助重力泄油（SAGD）过程；优化模型和方法在确定智能电网的高效储能和调度策略以及帮助确定风能和太阳能发电场的有效布局方面发挥着关键作用；定量建模和优化在交易（能源）金融衍生品时起着核心作用。许多数据驱动的问题可以表述或近似为线性优化问题。近年来在理论表述和计算性能方面都取得了实质性进展，包括对线性优化算法和整数优化模型的新颖分析。例如，获得了对单纯形法的见解，推翻了Hirsch猜想及其连续模拟，证明了中心路径跟踪方法是非强多项式的。

Data-driven analytics methodologies are presently at the forefront of efficient decision making and decision support in many industries. One prominent set of examples of this state-of-the-art optimization tools that made headway is optimizing energy generation, storage, transmission and delivery, and trading. These applications spread from operational to strategic time horizons. To name a few, optimization combined with other methods such as machine-learning is successfully used to improve the steam assisted gravity drainage (SAGD) process in oil recovery; optimization models and methods play a key role in determining efficient energy storage and dispatch strategies for smart grids, as well as help determine effective layouts for wind and solar farms; quantitative modelling and optimization occupy a central role when trading (energy) financial derivatives. Many data-driven problems can be formulated or approximated as linear optimization problems. There has been substantial progress in recent years in both the theoretical formulations and computational performances, including novel analysis of linear optimization algorithms and models for integer optimization. For instance, insights into the simplex method were obtained, Hirsch conjecture and its continuous analogue were disproved, and central-path following methods were shown to be non-strongly polynomial. Still there remains a dearth of work to further advance linear optimization theory and algorithms. This research proposal aims at searching for new ideas and extensions via the investigation of the strengths and limitations of currently used advanced algorithms. The methodology is based on a combination of novel constructions and worst-case examples, and advanced computational approaches to close the gap between the currently established lower and upper bounds. Worst-case instances appear in many contexts due to their extremal properties. For instance, the structures conjectured to maximize the diameter of lattice polytopes arise in the determination of the complexity of convex matroid optimization, and in the computation of the number of generalized retarded functions in quantum field theory. Combinatorial and high dimensional geometric properties are often unexpected. Computational experiments are therefore a key factor for identifying and proving theoretical properties. Another key focus of this research proposal is to develop new models to handle questions with applications in management sciences, supply-chain and transportation. Specifically, the proposal aims at further exploring optimization formulations to tackle question dealing with assemble-to-order (ATO) system and with shared electric vehicles. The objectives includes to further analyze the impact of component commonality for periodic review ATO systems, and to optimize the locations for charging stations for one-way electric car sharing programs by strategically locating charging stations given estimates of traffic flow.