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Trajectory optimization is becoming increasingly powerful in addressing motion planning problems of underactuated robotic systems. Numerous prior studies solve such a class of large non-convex optimal control problems in a hierarchical…
The deployment of Unmanned Aerial Vehicle (UAV) swarms as dynamic communication relays is critical for next-generation tactical networks. However, operating in contested environments requires solving a complex trade-off, including…
Accumulated Local Effect (ALE) is a method for accurately estimating feature effects, overcoming fundamental failure modes of previously-existed methods, such as Partial Dependence Plots. However, ALE's approximation, i.e. the method for…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…
We present ADMM-Softmax, an alternating direction method of multipliers (ADMM) for solving multinomial logistic regression (MLR) problems. Our method is geared toward supervised classification tasks with many examples and features. It…
We propose a continuous-time formulation of persistent contrastive divergence (PCD) for maximum likelihood estimation (MLE) of unnormalised densities. Our approach expresses PCD as a coupled, multiscale system of stochastic differential…
In this paper, we explore a novel approach to 3D anomaly detection (AD) that goes beyond merely identifying anomalies based on structural characteristics. Our primary perspective is that most anomalies arise from unpredictable defective…
Simultaneous localization and mapping (SLAM) systems with novel view synthesis capabilities are widely used in computer vision, with applications in augmented reality, robotics, and autonomous driving. However, existing approaches are…
In this paper, we develop a unified machine learning (ML) approach to predict high-quality solutions for single-machine scheduling problems with a non-decreasing min-sum objective function with or without release times. Our ML approach is…
This paper presents a simplified implementation of the arc-length method for computing the equilibrium paths of nonlinear structural mechanics problems using the finite element method. In the proposed technique, the predictor is computed by…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
Lesion detection is an important problem within medical imaging analysis. Most previous work focuses on detecting and segmenting a specialized category of lesions (e.g., lung nodules). However, in clinical practice, radiologists are…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
This work is devoted to the numerical simulation of nonlinear Schr\"odinger and Klein-Gordon equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency.…
Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed…
We propose a first-order method for solving inequality constrained optimization problems. The method is derived from our previous work [12], a modified search direction method (MSDM) that applies the singular-value decomposition of…
Identifying, measuring and reporting lesions accurately and comprehensively from patient CT scans are important yet time-consuming procedures for physicians. Computer-aided lesion/significant-findings detection techniques are at the core of…