Search
Search Results
-
Archimedean Representation Theorem for modules over a commutative ring
Pólya’s Positivstellensatz and Handelman’s Positivstellensatz are known to be concrete instances of the abstract Archimedean Representation Theorem...
-
Positivstellensätze for polynomial matrices
In this paper we establish some Positivstellensätze for polynomial matrices, applying the Scherer–Hol theorem. Firstly, we give a representation for...
-
Positivity on Polytopes
In this chapter we discuss certificates of positivity for polytopes, which are compact basic closed semialgebraic sets in...
-
Transitivity of Perspectivity
We study modules in which perspectivity of summands is transitive. Generalizing a 1977 result of Handelman and a 2014 result of Garg, Grover, and...
-
-
Handelman’s Positivstellensatz for polynomial matrices positive definite on polyhedra
In this paper we give a matrix version of Handelman’s Positivstellensatz (Handelman in Pac J Math 132:35–62,
1988 ), representing polynomial matrices... -
Relative Entropy Methods in Constrained Polynomial and Signomial Optimization
Relative entropy programs belong to the class of convex optimization problems. Within techniques based on the arithmetic-geometric mean inequality,...
-
Graded Cancellation Properties of Graded Rings and Graded Unit-regular Leavitt Path Algebras
We raise the following general question regarding a ring graded by a group: “If P is a ring-theoretic property, how does one define the graded...
-
-
Positivstellensätze for semirings
In this paper we develop a number of results and notions concerning Positivstellensätze for semirings (preprimes) of commutative unital real...
-
A new algorithm for concave quadratic programming
The main outcomes of the paper are divided into two parts. First, we present a new dual for quadratic programs, in which, the dual variables are...
-
Orbit Equivalence of Minimal Actions of a Finitely Generated Abelian Group
In measurable dynamics, the study of orbit equivalence, initiated by Dye [19], was developed by Krieger [56], Ornstein–Weiss [73] and...
-
Extended trust-region problems with one or two balls: exact copositive and Lagrangian relaxations
We establish a geometric condition guaranteeing exact copositive relaxation for the nonconvex quadratic optimization problem under two quadratic and...
-
Some Recent Developments in Spectrahedral Computation
Spectrahedra are the feasible sets of semidefinite programming and provide a central link between real algebraic geometry and convex optimization. In...
-
Rings with linearly ordered right annihilators
We introduce the class of lineal rings , defined by the property that the lattice of right annihilators is linearly ordered. We obtain results on the...
-
Handelman’s hierarchy for the maximum stable set problem
The maximum stable set problem is a well-known NP-hard problem in combinatorial optimization, which can be formulated as the maximization of a...
-
Finitely Stable Rings
A commutative ring R is finitely stable provided every finitely generated regular ideal of R is projective as a module over its ring of...
-
Noetherian Leavitt Path Algebras and Their Regular Algebras
In the past, it has been shown that the Leavitt path algebra L ( E ) = L K ( E ) of a graph E over a field K is left and right noetherian if and only if...
-
Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications
It has been observed that the Handelman’s certificate of positivity of a polynomial over a compact polyhedron offers a hierarchical relaxation scheme...
-
*-Regular Leavitt path algebras of arbitrary graphs
If K is a field with involution and E an arbitrary graph, the involution from K naturally induces an involution of the Leavitt path algebra L ...