[BOOK][B] An introduction to polynomial and semi-algebraic optimization
JB Lasserre - 2015 - books.google.com
This is the first comprehensive introduction to the powerful moment approach for solving
global optimization problems (and some related problems) described by polynomials (and …
global optimization problems (and some related problems) described by polynomials (and …
Quantifier elimination by cylindrical algebraic decomposition based on regular chains
A quantifier elimination algorithm by cylindrical algebraic decomposition based on regular
chains is presented. The main idea is to refine a complex cylindrical tree until the signs of …
chains is presented. The main idea is to refine a complex cylindrical tree until the signs of …
Choosing the variable ordering for cylindrical algebraic decomposition via exploiting chordal structure
H Li, B **a, H Zhang, T Zheng - Proceedings of the 2021 on International …, 2021 - dl.acm.org
Cylindrical algebraic decomposition (CAD) plays an important role in the field of real
algebraic geometry and many other areas. As is well-known, the choice of variable ordering …
algebraic geometry and many other areas. As is well-known, the choice of variable ordering …
On the complexity of the generalized MinRank problem
We study the complexity of solving the generalized MinRank problem, ie computing the set
of points where the evaluation of a polynomial matrix has rank at most r. A natural algebraic …
of points where the evaluation of a polynomial matrix has rank at most r. A natural algebraic …
Cylindrical algebraic decomposition using local projections
A Strzeboński - Proceedings of the 39th International Symposium on …, 2014 - dl.acm.org
We present an algorithm which computes a cylindrical algebraic decomposition of a
semialgebraic set using projection sets computed for each cell separately. Such local …
semialgebraic set using projection sets computed for each cell separately. Such local …
Probabilistic algorithm for polynomial optimization over a real algebraic set
A Greuet, M Safey El Din - SIAM Journal on Optimization, 2014 - SIAM
Let f,f_1,...,f_s be n-variate polynomials with rational coefficients of maximum degree D and
let V be the set of common complex solutions of F=(f_1,...,f_s). We give an algorithm which …
let V be the set of common complex solutions of F=(f_1,...,f_s). We give an algorithm which …
Refined f5 algorithms for ideals of minors of square matrices
We consider the problem of computing a grevlex Gröbner basis for the set Fr (M) of minors of
size r of an n× n matrix M of generic linear forms over a field of characteristic zero or large …
size r of an n× n matrix M of generic linear forms over a field of characteristic zero or large …
Choosing better variable orderings for cylindrical algebraic decomposition via exploiting chordal structure
H Li, B **a, H Zhang, T Zheng - Journal of Symbolic Computation, 2023 - Elsevier
As is well-known, the choice of variable ordering while computing cylindrical algebraic
decomposition (CAD) has a great effect on the time and memory use of the computation as …
decomposition (CAD) has a great effect on the time and memory use of the computation as …
Faster one block quantifier elimination for regular polynomial systems of equations
HP Le, M Safey El Din - Proceedings of the 2021 on International …, 2021 - dl.acm.org
Quantifier elimination over the reals is a central problem in computational real algebraic
geometry, polynomial system solving and symbolic computation. Given a semi-algebraic …
geometry, polynomial system solving and symbolic computation. Given a semi-algebraic …
Analytical and triangular solutions to operational flexibility analysis using quantifier elimination
The main purpose of operational flexibility analysis is to determine and describe the
flexibility region. The existing methods are mainly developed by numerical calculation …
flexibility region. The existing methods are mainly developed by numerical calculation …