Results 171 to 180 of about 1,163,681 (226)

Sum-of-squares hierarchies for binary polynomial optimization

Mathematical programming, 2020
We consider the sum-of-squares hierarchy of approximations for the problem of minimizing a polynomial f over the boolean hypercube $${{\mathbb {B}}^{n}=\{0,1\}^n}$$ B n = { 0 , 1 } n .
Lucas Slot, M. Laurent
semanticscholar   +1 more source

Robust H ∞ control for nonlinear course system of unmanned surface vessel with polytopic uncertainty based on sum of squares

Transactions of the Institute of Measurement and Control, 2020
In this paper, the nonlinear robust H ∞ control is investigated for nonlinear course control systems of unmanned surface vessel (USV) with uncertain parameters and external disturbance.
Yanwei Huang, Zhenyi Liu, Wenchao Huang, Shaobin Chen   +3 more
semanticscholar   +1 more source

Robust moment estimation and improved clustering via sum of squares

Symposium on the Theory of Computing, 2018
We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers and design a new family of convex relaxations for k-means clustering based on sum-of-squares method.
Pravesh Kothari, J. Steinhardt, David Steurer   +2 more
semanticscholar   +1 more source

Safe nonlinear control design for input constrained polynomial systems using sum-of-squares programming

International Journal of Control, 2020
We study the feedback stabilisation problem for input-affine polynomial systems subject to polytopic input constraints. First, we characterise a subset of the state-space, which we refer to as the stabilisation set, from where the system can be ...
Dimitrios Pylorof, E. Bakolas
semanticscholar   +1 more source

Sums of Two Squares of Sums of Two Squares

2016
This article determines the order of magnitude of integers not exceeding x that can be written as sums of two squares of integers that are themselves sums of two squares. The tools include Selberg’s sieve and contour integration in the spirit of the Selberg-Delange method.
openaire   +1 more source

Sums of Squares

1998
Our main aim in this chapter is to determine which integers can be expressed as the sum of a given number of squares, that is, which have the form where each xi e ℤ, for a given k. We shall concentrate mainly on the two most important cases, characterising the sums of two squares, and showing that every non-negative integer is a sum of four squares. We
Gareth A. Jones, J. Mary Jones
openaire   +1 more source

Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions

Journal of Optimization Theory and Applications, 2023
Xiangkai Sun, W. Tan, K. Teo
semanticscholar   +1 more source

Counting Sums of Three Squares

Bulletin of the London Mathematical Society, 1988
Let Q(x) denote the number of positive integers \(n\leq x\) which are sums of three squares, and let \(\Delta\) (x) be defined by \(Q(x)=5x/6+\Delta (x)\). \textit{E. Landau} [Arch. Math. Phys. 13, 303-312 (1908)] proved that \(\Delta (x)\ll \log x\) as \(x\to \infty\). \textit{N. C. Chakrabarti} [Bull. Calcutta Math. Soc.
openaire   +2 more sources

Sums of Squares

2022
  +4 more sources

CONISS: a FORTRAN 77 program for stratigraphically constrained cluster analysis by the method of incremental sum of squares

, 1987
E. Grimm
semanticscholar   +1 more source