Related papers: Calculation of extended gcd by normalization
We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT 4-approximation algorithm for the problem.
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for these ensembles the BDD problem is NP-hard in the worst case.…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…
Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms,…
Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two…
The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite difference like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve…
In this paper, a new iterative two-level algorithm is presented for solving the finite element discretization for nonsymmetric or indefinite elliptic problems. The iterative two-level algorithm uses the same coarse space as the traditional…
The normalized eight-point algorithm has been widely viewed as the cornerstone in two-view geometry computation, where the seminal Hartley's normalization has greatly improved the performance of the direct linear transformation algorithm. A…
We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…
We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti-Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes…
We propose a fully-corrective generalized conditional gradient method (FC-GCG) for the minimization of the sum of a smooth, convex loss function and a convex one-homogeneous regularizer over a Banach space. The algorithm relies on the…
Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process. Distributed and asynchronous variants of gradient descent have been…
In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local…