A characterization of the algebraic degree in semidefinite programming

被引：1

作者：

Hiep, Dang Tuan ^{[1
]}

Giao, Nguyen Thi Ngoc ^{[2
]}

Van, Nguyen Thi Mai ^{[3
]}

机构：

[1] Da Lat Univ, Fac Math & Comp Sci, 1 Phu Dong Thien Vuong, Da Lat, Lam Dong, Vietnam

[2] Univ Sci & Technol, Fac Adv Sci & Technol, Univ Da Nang, Da Nang, Vietnam

[3] Quy Nhon Univ, Fac Math & Stat, 170 An Duong Vuong, Quy Nhon, Binh Dinh, Vietnam

来源：

COLLECTANEA MATHEMATICA | 2023年 / 74卷 / 02期

关键词：

Schubert calculus; Algebraic degree; Semidefinite programming; GEOMETRY; FORMULA;

D O I：

10.1007/s13348-022-00358-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in a doubly symmetric polynomial. This characterization of the algebraic degree allows us to use the theory of symmetric polynomials to obtain many interesting results of Nie, Ranestad and Sturmfels in a simpler way.

引用

页码：443 / 455

页数：13

共 13 条

[1]

Cox DA., 1999, MATH SURVEYS MONOGRA, V68

[2] An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians [J].

Dang Tuan Hiep ;

Nguyen Chanh Tu .

JOURNAL OF ALGEBRA, 2021, 565 :564-581

[3] A FORMULA FOR THE ALGEBRAIC DEGREE IN SEMIDEFINITE PROGRAMMING [J].

Dang Tuan Hiep .

KODAI MATHEMATICAL JOURNAL, 2016, 39 (03) :484-488

[4]

Egge ES., 2019, INTRO SYMMETRIC FUNC, DOI [10.1090/stml/091, DOI 10.1090/STML/091]

[5] A general formula for the algebraic degree in semidefinite programming [J].

Graf von Bothmer, Hans-Christian ;

Ranestad, Kristian .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2009, 41 :193-197

[6] Sequences of Enumerative Geometry: Congruences and Asymptotics [J].

Grunberg, Daniel B. ;

Moree, Pieter ;

Zagier, Don .

EXPERIMENTAL MATHEMATICS, 2008, 17 (04) :409-426

[7] Identities involving (doubly) symmetric polynomials and integrals over Grassmannians [J].

Hiep, Dang Tuan .

FUNDAMENTA MATHEMATICAE, 2019, 246 (02) :181-191

[8] ON GIAMBELLI THEOREM ON COMPLETE CORRELATIONS [J].

LAKSOV, D ;

LASCOUX, A ;

THORUP, A .

ACTA MATHEMATICA, 1989, 162 (3-4) :143-199

[9]

MacDonald I.G., 1998, Symmetric Functions and Orthogonal Polynomials

[10]

Manivel L., 2020, ARXIV201108791

← 1 2 →