Results 261 to 270 of about 322,300 (286)

Chapter 3 Polynomial Optimization

2012
In this chapter, we consider the following polynomial optimization problem: \(f^{\ast} = {\text{min}} \{f(x) : x \in K\}\), where \(f \in \mathbb{R}[x]\) is a real-valued polynomial and \({\rm K}\,\subset \mathbb{R}^{n}\) is the basic semi-algebraic set defined by \(K = \{x \in \mathbb{R}^n : g_i(x) \geq 0, i=1,\ldots,m\}\), with \(g_i \in \mathbb{R}[x]
Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre   +2 more
openaire   +1 more source

Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization

Annual Reviews in Control, 2021
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou   +2 more
exaly  

Optimization with SOS Polynomials

2011
This chapter describes the use of SOS polynomials in typical optimization problems over polynomials. First, the case of unconstrained optimization is considered. It is shown how one can establish whether a polynomial is either positive or non-positive by introducing a generalized SOS index which measures how a polynomial is the ratio of two SOS ...
openaire   +1 more source

Chebyshev and Optimal Polynomials

1996
In this chapter we outline how to compute Chebyshev polynomials and certain closely related optimal polynomials for one interval and for the union of two disjoint intervals, respectively.
openaire   +1 more source

Optimization over polynomials

2014
Minimizing a polynomial function over a region defined by polynomial inequalitiesmodels broad classes of hard problems from combinatorics, geometry and optimization.New algorithmic approaches have emerged recently for computing the globalminimum, by combining tools from real algebra (sums of squares of polynomials) and functionalanalysis (moments of ...
openaire   +1 more source

CS-TSSOS: Correlative and Term Sparsity for Large-Scale Polynomial Optimization

ACM Transactions on Mathematical Software, 2022
Victor Magron, Jean Bernard Lasserre
exaly  

Robust motion trajectory optimization of overhead cranes based on polynomial chaos expansion

ISA Transactions, 2021
Haijun Peng, Xinwei Wang
exaly  

A Lagrange Multiplier Expression Method for Bilevel Polynomial Optimization

SIAM Journal on Optimization, 2021
Jiawang Nie, Jane J Ye
exaly  

Topology optimization under uncertainty via non-intrusive polynomial chaos expansion

Computer Methods in Applied Mechanics and Engineering, 2017
Vahid Keshavarzzadeh, Felipe Fernandez
exaly  

Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

SIAM Journal on Optimization, 2006
Hayato Waki
exaly