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Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…
We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations…
This paper presents a method for incorporating control analysis into design optimization for highly-maneuverable aircraft. By studying reachable sets for aircraft dynamics, we ensure that the optimizer will take the aircraft's controlled…
This article proposes a technique for the geometrically stable modeling of high-degree B-spline curves based on S-polygon in a float format, which will allow the accurate positioning of the end points of curves and the direction of the…
We show that the boundary curves (profiles) in $\R^2$ of the generalized projections of a body in $\R^3$ uniquely determine a large class of shapes, and that sparse profile data, combined with projection volume (brightness) data, can be…
By studying the existing higher order derivation formulas of rational B\'{e}zier curves, we find that they fail when the order of the derivative exceeds the degree of the curves. In this paper, we present a new derivation formula for…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
The notions of cutwidth and pathwidth of digraphs play a central role in the containment theory for tournaments, or more generally semi-complete digraphs, developed in a recent series of papers by Chudnovsky, Fradkin, Kim, Scott, and…
The proximal gradient method is a splitting algorithm for the minimization of the sum of two convex functions, one of which is smooth. It has applications in areas such as mechanics, inverse problems, machine learning, image reconstruction,…
In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…
Multi-directional 3D printing has the capability of decreasing or eliminating the need for support structures. Recent work proposed a beam-guided search algorithm to find an optimized sequence of plane-clipping, which gives volume…
Deep learning-based segmentation and classification are crucial to large-scale biomedical imaging, particularly for 3D data, where manual analysis is impractical. Although many methods exist, selecting suitable models and tuning parameters…
A key challenge for autonomous driving lies in maintaining real-time situational awareness regarding surrounding obstacles under strict latency constraints. The high processing requirements coupled with limited onboard computational…
Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable…
Leveraging on recent advancements on adaptive methods for convex minimization problems, this paper provides a linesearch-free proximal gradient framework for globalizing the convergence of popular stepsize choices such as Barzilai-Borwein…
We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers…
Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…
We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error function by scalar polynomials. The system of nonlinear…
This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic…