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The unit commitment problem (UC) is an optimization problem concerning the operation of electrical generators. Many algorithms have been proposed for the UC and in recent years a more decentralized approach, by solving the UC with…

Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

Trust-region (TR) and adaptive regularization using cubics (ARC) have proven to have some very appealing theoretical properties for non-convex optimization by concurrently computing function value, gradient, and Hessian matrix to obtain the…

In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…

The increasing penetration of renewable energy sources introduces significant uncertainty in power system operations, making traditional deterministic unit commitment approaches computationally expensive. This paper presents a machine…

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…

In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…

We focus on a simulation-based optimization problem of choosing the best design from the feasible space. Although the simulation model can be queried with finite samples, its internal processing rule cannot be utilized in the optimization…

Many studies are devoted to the design of radiomic models for a prediction task. When no effective model is found, it is often difficult to know whether the radiomic features do not include information relevant to the task or because of…

The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…

With increased reliance on cyber infrastructure, large scale power networks face new challenges owing to computational scalability. In this paper we focus on developing an asynchronous decentralized solution framework for the Unit…

This paper considers semi-supervised learning for tabular data. It is widely known that Xgboost based on tree model works well on the heterogeneous features while transductive support vector machine can exploit the low density separation…

The performance of particle advection-based flow visualization techniques is complex, since computational work can vary based on many factors, including number of particles, duration, and mesh type. Further, while many approaches have been…

It is well-known that deep learning models are vulnerable to adversarial examples. Existing studies of adversarial training have made great progress against this challenge. As a typical trait, they often assume that the class distribution…

The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…

Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…

Semi-supervised learning is pervasive in real-world applications, where only a few labeled data are available and large amounts of instances remain unlabeled. Since AUC is an important model evaluation metric in classification, directly…

We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For…

This paper presents a model-free reinforcement learning (RL) algorithm to solve the risk-averse optimal control (RAOC) problem for discrete-time nonlinear systems. While successful RL algorithms have been presented to learn optimal control…