We investigate quasi-Newton methods for minimizing a strongly convex quadratic function which is subject to errors in the evaluation of the gradients. In particular, we focus on computing search directions for quasi-Newton methods that all give identical behavior in exact arithmetic, generating minimizers of Krylov subspaces of increasing dimensions, thereby having finite termination. The BFGS quasi-Newton method may be seen as an ideal method in exact arithmetic and is empirically known to behave very well on a quadratic problem subject to small errors. We investigate large-error scenarios, in which the expected behavior is not so clear. We consider memoryless methods that are less expensive than the BFGS method, in that they generate low-rank quasi-Newton matrices that differ from the identity by a symmetric matrix of rank two. In addition, a more advanced model for generating the search directions is proposed, based on solving a chance-constrained optimization problem. Our numerical results indicate that for large errors, such a low-rank memoryless quasi-Newton method may perform better than a BFGS method. In addition, the results indicate a potential edge by including the chance-constrained model in the memoryless quasi-Newton method.

Support vector machines (SVM) is one of the well known supervised machine learning model. The standard SVM models are dealing with the situation where the exact values of the data points are known. This paper studies the SVM model when the data set contains uncertain or mislabelled data points. To ensure the small probability of misclassification for the uncertain data, a chance constrained conic-segmentation SVM model is proposed for multiclass classification. Based on the data set, a mixed integer programming formulation for the chance constrained conic-segmentation SVM is derived. Kernelization of chance constrained conic-segmentation SVM model is also exploited for nonlinear classification. The geometric interpretation is presented to show how the chance constrained conic-segmentation SVM works on uncertain data. Finally, experimental results are presented to demonstrate the effectiveness of the chance constrained conic-segmentation SVM for both artificial and real-world data.

Production logistics has an important role as a chain that connects the components of the production system. The most important goal of production logistics plans is to keep the flow of the production system well. However, compared to the production system, the level of planning, management, and digitalization of the production logistics system is not high enough, so it is difficult to respond flexibly when unexpected situations occur in the production logistics system. Optimization and heuristic algorithms have been proposed to solve this problem, but due to their inflexible nature, they can only achieve the desired solution in a limited environment. In this paper, the relationship between the production and production logistics system is analyzed and stochastic variables are introduced by modifying the pickup and delivery problem with time windows (PDPTW) optimization model to establish a flexible production logistics plan. This model, taking into account stochastic variables, gives the scheduler a new perspective, allowing them to have new insights based on the mathematical model. However, since the optimization model is still insufficient to respond to the dynamic environment, future research will cover how to derive meaningful results even in a dynamic environment such as a machine learning model. 

The COVID-19 pandemic has caused great disruption to the service sector, and it has, in turn, adapted by implementing measures that reduce physical contact among employees and users; examples include home-office work and the setting of occupancy restrictions at indoor locations. The design of services in the context of a pandemic requires balancing between two objectives: (i) special measures must be implemented to maintain physical separation among people to reduce the risk of infection, and (ii) these sanitary measures also reduce process capacity, thereby increasing the waiting times of users. We study this problem in the context of election processes, in which balancing waiting time with public safety is of first order relevance to ensuring voter turnout, using as a real-world application the Chilean 2020 national referendum. Analyzing this problem requires a multidisciplinary approach that consists of integrating randomized experiments to measure how voters weigh infection risk relative to waiting time and stochastic modeling/discrete event simulation to prescribe recommendations for the service design—specifically setting capacity limits to trade off between overcrowding and process efficiency. Overall, our results shows that infection risk is an important factor affecting voter turnout during a pandemic and that capacity limits can be a useful design tool to balance these risks with other service quality measures. Some of these findings were considered in the guidelines that Servel provided to manage capacity and voter arrival patterns at voting centers. 

In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We derive conditions under which we can generate a set of nested pits by varying the risk level instead of using revenue factors. We propose two properties that we believe are desirable for the problem: risk nestedness, which means the pits generated for different risk aversion levels should be contained in one another, and additive consistency, which states that preferences in terms of order of extraction should not change if independent sectors of the mine are added as precedences. We show that only an entropic risk measure satisfies these properties and propose a two-stage stochastic programming formulation of the problem, including an efficient approximation scheme to solve it. We illustrate our approach in a small self-constructed example, and apply our approximation scheme to a real-world section of the Andina mine, in Chile.