Related papers: Condition number bounds for problems with integer …
Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…
We study geometric characterizations of unbounded integer polynomial optimization problems. While unboundedness along a ray fully characterizes unbounded integer linear and quadratic optimization problems, we show that this is not the case…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions.…
The condition-based complexity analysis framework is one of the gems of modern numerical algebraic geometry and theoretical computer science. Among the challenges that it poses is to expand the currently limited range of random polynomials…
Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
Let Q be a non-singular quadratic form with integer coefficients. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q=0. When Q is positive definite we provide improved upper bounds…
Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are $\leq$ and $<$. Solving such constraints is an…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…
The problem of construction of the boundary conditions for nonlinear equations is considered compatible with their higher symmetries. Boundary conditions for the sine-Gordon, Jiber-Shabat and KdV equations are discussed. New examples are…
$f,g_1,...,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,...,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,...,m$.…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
We obtain upper bounds, independent of the ambient dimension, for the number of realizable zero-nonzero patterns and (over ordered fields) sign conditions of a finite family of polynomials $\mathcal P$ restricted to an algebraic subset $V$…