Related papers: External Incremental Delaunay Triangulation
In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric…
In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of…
A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…
A bi-level optimization framework (BiOPT) was proposed in [3] for convex composite optimization, which is a generalization of bi-level unconstrained minimization framework (BLUM) given in [20]. In this continuation paper, we introduce a…
We present a novel 2D convex hull peeling algorithm for outlier detection, which repeatedly removes the point on the hull that decreases the hull's area the most. To find k outliers among n points, one simply peels k points. The algorithm…
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…
This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…
The problem of computing the exact stretch factor (i.e., the tight bound on the worst case stretch factor) of a Delaunay triangulation is one of the longstanding open problems in computational geometry. Over the years, a series of upper and…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasinonexpansive operators…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
Dense random sampling and surfacing of shapes encoded via implicit occupancy functions (OFs) are critical elements of many applications. Existing methods largely provide either one or the other of random sampling or mesh surfaces: ray…
Interpolating unstructured data using barycentric coordinates becomes infeasible at high dimensions due to the prohibitive memory requirements of building a Delaunay triangulation. We present a new algorithm to construct ad-hoc simplices…
This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…
Several techniques were proposed to model the Piecewise linear (PWL) functions, including convex combination, incremental and multiple choice methods. Although the incremental method was proved to be very efficient, the attention of the…
We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…