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This manuscript extends the relaxation theory from nonlinear elasticity to electromagnetism and to actions defined on paths of differential forms. The introduction of a gauge allows for a reformulation of the notion of quasiconvexity in Bandyopadhyay et al ...
The ever-increasing utilization of sensitive loads in the industrial, commercial, and residential areas in distribution networks requires enhanced reliability and quality of supply. This can be achieved, thanks to self-healing features of smart grids that ...
Large horsepower induction motors play a critical role as industrial drives in production facilities. The operational safety of distribution networks during the starting transients of these motor loads is a critical concern for the operators. In this paper ...
With the ever-growing data sizes along with the increasing complexity of the modern problem formulations, contemporary applications in science and engineering impose heavy computational and storage burdens on the optimization algorithms. As a result, there ...
Optimization models for long-term energy planning often feature many uncertain inputs, which can be handled using robust optimization. However, uncertainty is seldom accounted for in the energy planning practice, and robust optimization applications in thi ...
Plain vanilla K-means clustering is prone to produce unbalanced clusters and suffers from outlier sensitivity. To mitigate both shortcomings, we formulate a joint outlier-detection and clustering problem, which assigns a prescribed number of datapoints to ...
An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius ρ such that there exist balls of radius ρ around ...
We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy techniques to ha ...
Dense conditional random fields (CRFs) have become a popular framework for modeling several problems in computer vision such as stereo correspondence and multiclass semantic segmentation. By modeling long-range interactions, dense CRFs provide a labeling t ...
A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed fo ...