Integer Polynomial Optimization in Fixed Dimension
نویسندگان
چکیده
منابع مشابه
Integer Polynomial Optimization in Fixed Dimension
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials t...
متن کاملFast Integer Programming in Fixed Dimension
It is shown that the optimum of an integer program in fixed dimension with a fixed number of constraints can be computed with O(s) basic arithmetic operations, where s is the binary encoding length of the input. This improves on the quadratic running time of previous algorithms, which are based on Lenstra’s algorithm and binary search. It follows that an integer program in fixed dimension, whic...
متن کاملParametric Integer Programming in Fixed Dimension
We consider the following problem: Given a rational matrix A ∈ Qm×n and a rational polyhedron Q ⊆ Rm+p, decide if for all vectors b ∈ Rm, for which there exists an integral z ∈ Zp such that (b,z) ∈ Q, the system of linear inequalities Ax 6 b has an integral solution. We show that there exists an algorithm that solves this problem in polynomial time if p and n are fixed. This extends a result of...
متن کاملComplexity of integer quasiconvex polynomial optimization
We study a particular case of integer polynomial optimization: Minimize a polynomial F̂ on the set of integer points described by an inequality system F1 ≤ 0, . . . , Fs ≤ 0, where F̂ , F1, . . . , Fs are quasiconvex polynomials in n variables with integer coefficients. We design an algorithm solving this problem that belongs to the time-complexity class O(s) · lO(1) · dO(n) · 2O(n 3), where d ≥ ...
متن کاملDimension of Automorphisms with Fixed Degree for Polynomial Algebras
Let K[x, y] be the polynomial algebra in two variables over an algebraically closed field K. We generalize to the case of any characteristic the result of Furter that over a field of characteristic zero the set of automorphisms (f, g) of K[x, y] such that max{deg(f), deg(g)} = n ≥ 2 is constructible with dimension n + 6. The same result holds for the automorphisms of the free associative algebr...
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: Mathematics of Operations Research
سال: 2006
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.1050.0169