Related papers: Remark on the Smale's Problem 9
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
The following four classes of computational problems are equivalent: solving matrix games, solving linear programs, best $l^{\infty}$ linear approximation, best $l^1$ linear approximation.
Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…
The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that…
This paper has been withdrawn because Theorem 21 and Corollary 22 are in error; The modeling idea is OK, but it needs 9-dimensional variables instead of the 8-dimensional variables defined in notations 6.9. Examples of the correct model…
The goal of this paper is to present an overview of the software collection for the solution of linear and nonlinear semidefinite optimization problems PENNON. In the first part we present theoretical and practical details of the underlying…
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…
In this paper we obtain a partial answer to a conjecture on the solvabilty of linear difference equations in quasianalytic Carleman classes.
In this note we give an explicit parametrization of the modular curve associated to the normalizer of a non-split Cartan subgroup of level 9. We determine all integral points of this modular curve. As an application, we give an alternative…
The 0-1 linear programming problem with nonnegative constraint matrix and objective vector e origins from many NP-hard combinatorial optimization problems. In this paper, we consider recovering an optimal solution to the problem from a…
In this article we consider a method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program.
We consider 9 natural tightness conditions for topological spaces that are all variations on countable tightness and investigate the interrelationships between them. Several natural open problems are raised.
We prove doubling inequalities for solutions of elliptic systems with an iterated Laplacian as diagonal principal part and for solutions of the Lame' system of isotropic linearized elasticity. These inequalities depend on global properties…
We associate with any simplicial complex $\K$ and any integer $m$ a system of linear equations and inequalities. If $\K$ has a simplicial embedding in $\R^m$ then the system has an integer solution. This result extends the work of I. Novik…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…