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We consider a risk-averse stochastic capacity planning problem under uncertain demand in each period. Using a scenario tree representation of the uncertainty, we formulate a multistage stochastic integer program to adjust the capacity expansion plan dynamically as more information on the uncertainty is revealed. Specifically, in each stage, a decision maker optimizes capacity acquisition and resource allocation to minimize certain risk measures of maintenance and operational cost. We compare it with a two-stage approach that determines the capacity acquisition for all the periods up front. Using expected conditional risk measures, we derive a tight lower bound and an upper bound for the gaps between the optimal objective values of risk-averse multistage models and their two-stage counterparts. Based on these derived bounds, we present general guidelines on when to solve risk-averse two-stage or multistage models. Furthermore, we propose approximation algorithms to solve the two models more efficiently, which are asymptotically optimal under an expanding market assumption. We conduct numerical studies using randomly generated and real-world instances with diverse sizes, to demonstrate the tightness of the analytical bounds and efficacy of the approximation algorithms. We find that the gaps between risk-averse multistage and two-stage models increase as the variability of the uncertain parameters increases and decrease as the decision maker becomes more risk averse. Moreover, a stagewise-dependent scenario tree attains much higher gaps than a stagewise-independent counterpart, whereas the latter produces tighter analytical bounds. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work of Dr. X. Yu was partially supported by the U.S. National Science Foundation Division of Information and Intelligent Systems [Grant 2331782]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0396 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0396 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ . 

Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy minimization and circuit compilation. In this paper we focus on discrete binary quantum control problems and apply different optimization algorithms and techniques to improve computational efficiency and solution quality. Specifically, we develop a generic model and extend it in several ways. We introduce a squared $L_2$-penalty function to handle additional side constraints, to model requirements such as allowing at most one control to be active. We introduce a total variation (TV) regularizer to reduce the number of switches in the control. We modify the popular gradient ascent pulse engineering (GRAPE) algorithm, develop a new alternating direction method of multipliers (ADMM) algorithm to solve the continuous relaxation of the penalized model, and then apply rounding techniques to obtain binary control solutions. We propose a modified trust-region method to further improve the solutions. Our algorithms can obtain high-quality control results, as demonstrated by numerical studies on diverse quantum control examples.