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During spinal fusion surgery, screws are placed close to critical nerves suggesting the need for highly accurate screw placement. Verifying screw placement on high-quality tomographic imaging is essential. C-arm Cone-beam CT (CBCT) provides…
We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: the…
In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…
It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao et.al. (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a…
In this paper, we give a quadratic Goldreich-Levin algorithm that is close to optimal in the following ways. Given a bounded function $f$ on the Boolean hypercube $\mathbb{F}_2^n$ and any $\varepsilon>0$, the algorithm returns a quadratic…
Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure --…
We present a fast convolution-based technique for computing an approximate, signed Euclidean distance function $S$ on a set of 2D and 3D grid locations. Instead of solving the non-linear, static Hamilton-Jacobi equation ($\|\nabla S\|=1$),…
Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and…
We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…
This research proposes a computation approach to address the evaluation of end product machining accuracy in elliptical surfaced helical pipe bending using 6dof parallel manipulator as a pipe bender. The target end product is wearable metal…
This study presents a novel approach for reconstructing cone beam computed tomography (CBCT) for specific orbits using known operator learning. Unlike traditional methods, this technique employs a filtered backprojection type (FBP-type)…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a…
We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is $\frac{4}{3}$, which matches the current best ratio. The approximation ratio of the algorithm is $\frac{6}{5}$…
In this paper a new hp-adaptive strategy for elliptic problems based on refinement history is proposed, which chooses h-, p- or hp-refinement on individual elements according to a posteriori error estimate, as well as smoothness estimate of…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…