Optimization and Moments
TruncatedTMomentMatrix(type,n,d)
returns the matrix of moments up to degree d of n-variate polynomials in the basis of Chebyshev polynomials
-type: simple Lie type
-n, d: posint
| > | TMomentMatrix(G,2,1); |
 |
(5.1) |
THermiteMatrix(type,n)
returns the Hermite matrix polynomial HermiteMatrix(type,n) in the basis of generalized Chebyshev polynomials of the first kind
-type: simple Lie type
-n: posint
| > | THermiteMatrix(G,2); |
 |
(5.2) |
TLocalizedPMI(type,n,d)
returns the localized moment matrix at HermiteMatrix(type,n) for the moment relaxation up to degree d
Warning: This takes a while!
-type: simple Lie type
-n, d: posint
| > | TLocalizedMomentMatrix(G,2,2); |
                                                                                |
(5.3) |
ChebyshevSDPdata(type,n,d,name,c)
creates a csv file "name.csv" containing the SDP data [A_0, (A_1, ..., A_m), c] for the primal-dual moment relaxation up to degree d.
m + 1 = binomial(n+2*d,n) is the number of variables of the relaxation
(P) min Trace(A_0 * X) (D) max c^t * y
s.t. X symm. p.s.d. s.t. y in R^m
Trace(A_i * X) = c_i A_0 +y_1 A_1 + ... + y_m A_m is p.s.d.
Remark: This takes a while so maybe start with n=3, d=3! And remove the "#".
Warning: This creates a file in the folder of this worksheet!
Please read the Maple worksheet "generating_SDP_data" available under https://github.com/TobiasMetzlaff/GeneralizedChebyshev/blob/main/Maple%20Worksheets/generating_SDP_data.mw for instructions on how to produce and use the files in general.
-type: simple Lie type
-n, d: posint, d>=n
-name: string
-c: list
| > | Type:=B: n:=3: d:=3:
#SDPMatrices(Type,n,d,"B3Deg3.csv"); |