Algebraic Degree of Polynomial Optimization
نویسندگان
چکیده
منابع مشابه
Algebraic Degree of Polynomial Optimization
Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, we prove that the optimality conditions always hold on optimizers, and the coordinates of optimizers are algebraic functions of the coefficients of the input polynomials. We also give a general formula for the algebraic degree of the opti...
متن کاملThe Algebraic Degree of Geometric Optimization Problems
AJ1STRACT In this paper we apply Galois theoretic algebraic methods to certain fundamental geometric optimization problems whose recognition versions are not even known to be in the class NP. In particular we show that the classic Weber problem, the Line-restricted' Weber probe lem and the 3-Dimension version of this problem are in general not solvable by radicals over the field of rationals. O...
متن کاملAlgebraic adjoint of the polynomials-polynomial matrix multiplication
This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field
متن کاملReal algebraic numbers and polynomial systems of small degree
Based on precomputed Sturm-Habicht sequences, discriminants and invariants, we classify, isolate with rational points, and compare the real roots of polynomials of degree up to 4. In particular, we express all isolating points as rational functions of the input polynomial coefficients. Although the roots are algebraic numbers and can be expressed by radicals, such representation involves some r...
متن کاملProbabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set
Let f, f1, . . . , fs be n-variate polynomials with rational coefficients of maximum degree D and let V be the set of common complex solutions of F = (f1, . . . , fs). We give an algorithm which, up to some regularity assumptions on F, computes an exact representation of the global infimum f? of the restriction of the map x → f (x) to V ∩ Rn, i.e. a univariate polynomial vanishing at f? and an ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2009
ISSN: 1052-6234,1095-7189
DOI: 10.1137/080716670