Related papers: The central curve in linear programming
We recover the first linear programming bound of McEliece, Rodemich, Rumsey, and Welch for binary error-correcting codes and designs via a covering argument. It is possible to show, interpreting the following notions appropriately, that if…
We study the matrix factorizations defined by the generic plane projections of a curve singularity of $\mathbb{C}^3$. On the other hand, given a plane curve singularity $Y\subset \mathbb{C}^2$ we study the family of matrix factorizations…
In this paper, we analyze the planar cubic Alternative curve to determine the conditions for convex, loops, cusps and inflection points. Thus cubic curve is represented by linear combination of three control points and basis function that…
Cone regression is a particular case of quadratic programming that minimizes a weighted sum of squared residuals under a set of linear inequality constraints. Several important statistical problems such as isotonic, concave regression or…
The entropic discriminant is a non-negative polynomial associated to a matrix. It arises in contexts ranging from statistics and linear programming to singularity theory and algebraic geometry. It describes the complex branch locus of the…
Classical existence theorems and solution methods for quadratic programming traditionally rely on the analytical properties of real numbers, specifically compactness and completeness. These tools are unavailable in general linearly ordered…
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective…
The arrow graph of a function consists of two parallel axes, with arrows from input values to output values. The lines through these arrows envelop a curve which we named the focal curve. This paper studies these focal curves in detail. We…
A metrized complex of algebraic curves is a finite metric graph together with a collection of marked complete nonsingular algebraic curves, one for each vertex, the marked points being in bijection with incident edges. We establish a…
The characterization of local regularity is a fundamental issue in signal and image processing, since it contains relevant information about the underlying systems. The 2-microlocal frontier, a monotone concave downward curve in $\mathbb…
The definition of factor space and a unified optimization based classification model were developed for linear programming. Intelligent behaviour appeared in a decision process can be treated as a point y, the dynamic state observed and…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none…
For a smooth plane cubic $B$, we count curves $C$ of degree $d$ such that the normalizations of $C\backslash B$ are isomorphic to $\Bbb A^1$, for $d\leq7$ (for $d=7$ under some assumption). We also count plane rational quartic curves…
We define a plane curve to be threadable if it can rigidly pass through a point-hole in a line L without otherwise touching L. Threadable curves are in a sense generalizations of monotone curves. We have two main results. The first is a…
To solve a linear program, the simplex method follows a path in the graph of a polytope, on which a linear function increases. The length of this path is an key measure of the complexity of the simplex method. Numerous previous articles…
For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane closed curve whose chord diagram contains the given chord diagram as a…
The core of an ideal is the intersection of all its reductions. For large classes of ideals I we explicitly describe the core as a colon ideal of a power of a single reduction and a power of I.
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…