An Arbitrary Starting Homotopy-Like Simplicial Algorithm for Computing an Integer Point in a Class of Polytopes

2009 ◽  
Vol 23 (2) ◽  
pp. 609-633 ◽  
Author(s):  
Chuangyin Dang
Keyword(s):  
Integer Point ◽  
Simplicial Algorithm

scholarly journals Scanning integer points with lex-inequalities: a finite cutting plane algorithm for integer programming with linear objective

4OR ◽  
2020 ◽  
Author(s):  
Michele Conforti ◽  
Marianna De Santis ◽  
Marco Di Summa ◽  
Francesco Rinaldi
Keyword(s):  
Integer Point ◽  
Cutting Plane ◽  
Integer Program ◽  
Compact Set ◽  
Cutting Plane Method ◽  
Integer Points ◽  
Gomory Cuts ◽  
The Family ◽  
Split Cuts ◽  
Number Of Iterations

AbstractWe consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that define the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-inequalities contains the Chvátal–Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program $$\min \{cx: x\in S\cap \mathbb {Z}^n\}$$ min { c x : x ∈ S ∩ Z n } , where $$S\subset \mathbb {R}^n$$ S ⊂ R n is a compact set and $$c\in \mathbb {Z}^n$$ c ∈ Z n . We analyze the number of iterations of our algorithm.

Triangulating between parallel splitting contours using a simplicial algorithm

1991 ◽  
Author(s):  
Rick Miranda ◽  
Thomas O. McCracken ◽  
Chris Fedde
Keyword(s):  
Simplicial Algorithm ◽  
Parallel Splitting

scholarly journals A Family of Integer-Point Ternary Parametric Subdivision Schemes

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ghulam Mustafa ◽  
Muhammad Asghar ◽  
Shafqat Ali ◽  
Ayesha Afzal ◽  
Jia-Bao Liu
Keyword(s):  
General Formula ◽  
Integer Point ◽  
Laurent Polynomial ◽  
Polynomial Method ◽  
Subdivision Schemes ◽  
Smooth Curves ◽  
Curves And Surfaces

New subdivision schemes are always required for the generation of smooth curves and surfaces. The purpose of this paper is to present a general formula for family of parametric ternary subdivision schemes based on the Laurent polynomial method. The different complexity subdivision schemes are obtained by substituting the different values of the parameter. The important properties of the proposed family of subdivision schemes are also presented. The continuity of the proposed family is C 2 m . Comparison shows that the proposed family of subdivision schemes has higher degree of polynomial generation, degree of polynomial reproduction, and continuity compared with the exiting subdivision schemes. Maple software is used for mathematical calculations and plotting of graphs.

scholarly journals Bounds for the smallest integer point of a rational curve

2003 ◽  
Vol 107 (3) ◽  
pp. 251-268
Author(s):  
Dimitrios Poulakis
Keyword(s):  
Integer Point ◽  
Rational Curve

scholarly journals Schubert polynomials as integer point transforms of generalized permutahedra

2018 ◽  
Vol 332 ◽  
pp. 465-475 ◽  
Author(s):  
Alex Fink ◽  
Karola Mészáros ◽  
Avery St. Dizier
Keyword(s):  
Integer Point ◽  
Schubert Polynomials

SYMMETRIC MULTIVARIATE WAVELETS

2009 ◽  
Vol 07 (03) ◽  
pp. 313-340 ◽  
Author(s):  
S. KARAKAZ'YAN ◽  
M. SKOPINA ◽  
M. TCHOBANOU
Keyword(s):  
Arbitrary Order ◽  
Integer Point ◽  
Explicit Method ◽  
Explicit Formulas ◽  
Arbitrary Matrix ◽  
Vanishing Moments ◽  
Compactly Supported ◽  
Matrix Dilation

For arbitrary matrix dilation M whose determinant is odd or equal to ±2, we describe all symmetric interpolatory masks generating dual compactly supported wavelet systems with vanishing moments up to arbitrary order n. For each such mask, we give explicit formulas for a dual refinable mask and for wavelet masks such that the corresponding wavelet functions are real and symmetric/antisymmetric. We proved that an interpolatory mask whose center of symmetry is different from the origin cannot generate wavelets with vanishing moments of order n > 0. For matrix dilations M with | det M| = 2, we also give an explicit method for construction of masks (non-interpolatory) m0 symmetric with respect to a semi-integer point and providing vanishing moments up to arbitrary order n. It is proved that for some matrix dilations (in particular, for the quincunx matrix) such a mask does not have a dual mask. Some of the constructed masks were successfully applied for signal processes.

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