I want to know where my problem is?

Nonconvex
1

I was recently solving the norm constraint problem using CVX, but the following error occurred

> clc
> clear
> S=[0	1
>    1	0];
> R=[1	0];
> T=30;
> x1=[-2.10223695603323	-3.78591992632920	-7.17269955056974	-18.6477140679511	-41.6973303472063	-83.9775248787705	-171.991480897492	-349.597102022052	-699.927895858096	-1401.64892366758	-2804.46098955305	-5610.77236359478	-11222.8441395386	-22449.1703286641	-44898.9833630878	-89794.8407299650	-179592.689380526	-359186.773382450	-718374.821910199	-1436748.06696509	-2873496.00051562	-5746985.53438892	-11493961.6330137	-22987923.3966060	-45975851.0972372	-91951699.3265585	-183903401.530448	-367806801.737505	-735613601.046596	-1471227200.40138	-2942454396.37478];
> x11=[-2.10223695603323	-3.78591992632920	-7.17269955056974	-18.6477140679511	-41.6973303472063	-83.9775248787705	-171.991480897492	-349.597102022052	-699.927895858096	-1401.64892366758	-2804.46098955305	-5610.77236359478	-11222.8441395386	-22449.1703286641	-44898.9833630878	-89794.8407299650	-179592.689380526	-359186.773382450	-718374.821910199	-1436748.06696509	-2873496.00051562	-5746985.53438892	-11493961.6330137	-22987923.3966060	-45975851.0972372	-91951699.3265585	-183903401.530448	-367806801.737505	-735613601.046596	-1471227200.40138];
> x12=[-3.78591992632920	-7.17269955056974	-18.6477140679511	-41.6973303472063	-83.9775248787705	-171.991480897492	-349.597102022052	-699.927895858096	-1401.64892366758	-2804.46098955305	-5610.77236359478	-11222.8441395386	-22449.1703286641	-44898.9833630878	-89794.8407299650	-179592.689380526	-359186.773382450	-718374.821910199	-1436748.06696509	-2873496.00051562	-5746985.53438892	-11493961.6330137	-22987923.3966060	-45975851.0972372	-91951699.3265585	-183903401.530448	-367806801.737505	-735613601.046596	-1471227200.40138	-2942454396.37478];
> U1=[0.0839020868032457	0.271850670637684	-1.26028094217183	-1.31612689629908	-0.137268536575792	-1.22896532115407	-1.72581923496823	-0.0428677342217937	-0.434584472240198	-0.410603771339194	-0.506073363949543	-0.219681917094316	-0.930567709270003	-0.251253845566330	1.15390495264716	-1.07309584968435	-0.395734923392060	-0.441914027334909	0.383637720895366	-0.0793911172296072	2.14061528349563	2.93145024266009	0.160664624331637	-1.48647399970287	1.03398849842491	-0.970312982615375	0.495165059700248	0.908498454030357	0.496875690466906	1.65011538655992];
> Y1=[-2.10223695603323	-3.78591992632920	-7.17269955056974	-18.6477140679511	-41.6973303472063	-83.9775248787705	-171.991480897492	-349.597102022052	-699.927895858096	-1401.64892366758	-2804.46098955305	-5610.77236359478	-11222.8441395386	-22449.1703286641	-44898.9833630878	-89794.8407299650	-179592.689380526	-359186.773382450	-718374.821910199	-1436748.06696509	-2873496.00051562	-5746985.53438892	-11493961.6330137	-22987923.3966060	-45975851.0972372	-91951699.3265585	-183903401.530448	-367806801.737505	-735613601.046596	-1471227200.40138	-2942454396.37478];
> X1_1=pinv(x1);
> E11=[U1;x11];
> E11=pinv(E11);
>  cvx_begin 
>     cvx_solver  sdpt3
>     variable MEN1(1, 2) 
>     variable TAO1(1, 2) 
>     variable W1(1, 30) 
>     minimize (norm((x12-W1)*E11*[TAO1;MEN1]-MEN1*S,F))
>     minimize (norm(Y1*X1_1*MEN1-R,F))
>     subject to
>     W1*W1'<= T*0.5*eye(1);
>  cvx_end

The matrix is known except for the three variables defined, F represents the F norm, and the error is as follows

ill usage *
Disciplined convex programming error:
Only scalar quadratic forms can be specified in CVX
.

2

The proper syntax for the F norm is ‘fro’`.

Your 2nd minimize would be accepted by CVX. Although only one minimize or maximize is allowed between cvx_begin and cvx_end.

Your first minimize produces the error message because it involves the multiplication of variables W1 and MEN. Moreover, the argument of norm must be affine.