On Cones of Nonnegative Quadratic Functions

By Jos F. Sturm, Shuzhong Zhang. Mathematics of Operations Research, 2003

381 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/50109b49c2ecfba79dbd4ec0e2c53b756a15ae96

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

On the copositive representation of binary and continuous nonconvex quadratic programs (2009, background): “[3] and Sturm and Zhang [18] (see Sect.”
The power of localization for efficiently learning linear separators with noise (2013, methodology): “Since − X T X is symmetric, problems of this form are known to be solv-able in polynomial time [40] (see [12]).”
Positivity of Riesz Functionals and Solutions of Quadratic and Quartic Moment Problems (2009, methodology): “When f(x) and g(x) are homogeneous and quadratic, if f(x) is nonnegative on the algebraic set E(q) = {x ∈ Rn : q(x) = 0}, then a certificate like that provided by S-Lemma holds, but without requiring t ≥ 0, as pointed out by Luo, Sturm and Zhang [15].”
Recent advances in trust region algorithms (2015, methodology): “Properties of the CDT subproblem are discussed by many authors [2,19,87,116,144], and algorithms for solving the CDT subproblem are given by [145,156].”
Application of the Moment-SOS Approach to Global Optimization of the OPF Problem (2013, background): “They discard the rank constraint, as it is done in Shor’s relaxation [8], a well-known procedure which applies to quadratically constrained quadratic problems (see [9], [10] and the references therein).”
Detecting global optimality and extracting solutions in GloptiPoly (2003, methodology): “A specic extraction procedure was also described in [ 19, Section 5 ] in the case of quadratic optimization problems with one (possibly non-convex) quadratic constraint, or one linear constraint jointly with one concave quadratic constraint.”