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We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…
The area under the ROC curve (AUC) is a measure of interest in various machine learning and data mining applications. It has been widely used to evaluate classification performance on heavily imbalanced data. The kernelized AUC maximization…
A time-dependent global fiber-bundle model of fracture with continuous damage was recently formulated in terms of an autonomous differential system and numerically solved by applying a discrete probabilistic method. In this paper we provide…
Many machine learning problems can be formulated as consensus optimization problems which can be solved efficiently via a cooperative multi-agent system. However, the agents in the system can be unreliable due to a variety of reasons:…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
When numerically solving partial differential equations, for a given problem and operating condition, adaptive mesh refinement (AMR) has proven its efficiency to automatically build a discretization achieving a prescribed accuracy at low…
In this work, we propose some new Douglas-Rashford splitting algorithms for solving a class of generalized DC (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal properties of the nonsmooth…
The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension…
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be…
Unsupervised anomaly detection (UAD) learns one-class classifiers exclusively with normal (i.e., healthy) images to detect any abnormal (i.e., unhealthy) samples that do not conform to the expected normal patterns. UAD has two main…
We propose a novel computational method for unit commitment UC, which does not require linearized approximation and provides several orders of magnitude performance improvement over current state-of-the-art. The performance improvement is…
In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…
This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique…
This paper investigates the localization problem of high-speed high-altitude unmanned aerial vehicle (UAV) with a monocular camera and inertial navigation system. It proposes a navigation method utilizing the complementarity of vision and…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
In Continual Learning (CL), while existing work primarily focuses on the multi-class classification task, there has been limited research on Multi-Label Learning (MLL). In practice, MLL datasets are often class-imbalanced, making it…
This paper introduces a nonlinear conjugate gradient method (NCGM) for addressing the robust counterpart of uncertain multiobjective optimization problems (UMOPs). Here, the robust counterpart is defined as the minimum across objective-wise…
Variational inequalities play a pivotal role in a wide array of scientific and engineering applications. This project presents two techniques for adaptive mesh refinement (AMR) in the context of variational inequalities, with a specific…
The parallel alternating direction method of multipliers (ADMM) algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical…
In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…