Semidefinite Relaxation and New Conditions for Sign-Definiteness of the Quadratic Form under Quadratic Constraints

2018 ◽  
Vol 79 (11) ◽  
pp. 2073-2079 ◽  
Author(s):  
L. B. Rapoport
Keyword(s):  
Quadratic Form ◽  
Semidefinite Relaxation ◽  
Quadratic Constraints ◽  
Sign Definiteness

Polynomial Definiteness and Semidefiniteness

1970 ◽  
Vol 92 (2) ◽  
pp. 394-397 ◽  
Author(s):  
Chiou-Shiun Chen ◽  
Edwin Kinnen
Keyword(s):  
Quadratic Form ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Real Polynomial ◽  
Reduction Procedure ◽  
Sign Definiteness ◽  
Order Polynomial ◽  
The Individual ◽  
New Variables ◽  
Engineering Stability

A reduction procedure is described for determining the sign definiteness and semidefiniteness of an mth order, n dimensional real polynomial. The higher order polynomial is reduced to a quadratic form in new variables such that conditions can be obtained on the coefficients of the individual terms of the original polynomial. The procedure presents sufficient conditions only. It has been found, however, to be a relatively systematic technique for engineering stability problems where alternate effective methods for determining sign definiteness are unknown.

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