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Deep neural networks (DNNs) have become one of the enabling technologies in many safety-critical applications, e.g., autonomous driving and medical image analysis. DNN systems, however, suffer from various kinds of threats, such as…
A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
Energy saving is becoming an important issue in the design and use of computer networks. In this work we propose a problem that considers the use of rate adaptation as the energy saving strategy in networks. The problem is modeled as an…
We present necessary and sufficient conditions for solving the strongly dependent decision (SDD) problem in various distributed systems. Our main contribution is a novel characterization of the SDD problem based on point-set topology. For…
Order picking is a pivotal operation in warehouses that directly impacts overall efficiency and profitability. This study addresses the dynamic order picking problem, a significant concern in modern warehouse management, where real-time…
Dantzig-Wolfe decomposition (DWD) is a classical algorithm for solving large-scale linear programs whose constraint matrix involves a set of independent blocks coupled with a set of linking rows. The algorithm decomposes such a model into a…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
A recently new intelligent optimization algorithm called discrete state transition algorithm is considered in this study, for solving unconstrained integer optimization problems. Firstly, some key elements for discrete state transition…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
Probabilistic methods have attracted much interest in fault detection design, but its need for complete distributional knowledge is seldomly fulfilled. This has spurred endeavors in distributionally robust fault detection (DRFD) design,…
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We…
Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly…
This paper develops a novel differentially private framework to solve convex optimization problems with sensitive optimization data and complex physical or operational constraints. Unlike standard noise-additive algorithms, that act…
With the extensive integration of volatile and uncertain renewable energy, power systems face significant challenges in primary frequency regulation due to instantaneous power fluctuations. However, the maximum frequency deviation…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…
Deletion Propagation (DP) refers to a family of database problems rooted in the classical view-update problem: how to propagate intended deletions in a view (query output) back to the source database while satisfying constraints and…
Large optimization problems with hard constraints arise in many settings, yet classical solvers are often prohibitively slow, motivating the use of deep networks as cheap "approximate solvers." Unfortunately, naive deep learning approaches…
Learning in MDPs with highly complex state representations is currently possible due to multiple advancements in reinforcement learning algorithm design. However, this incline in complexity, and furthermore the increase in the dimensions of…