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There is nothing more practical than a good theory.

1d
accepted Positive solutions of linear systems with a diagonally dominant matrix
Jan
27
answered What's the most efficient way to solve this euclidean projection on non-negative affine space constraint?
Jan
14
revised Positive solutions of linear systems with a diagonally dominant matrix
added 163 characters in body
Jan
14
asked Positive solutions of linear systems with a diagonally dominant matrix
Jan
13
awarded  Necromancer
Sep
24
awarded  Autobiographer
Aug
28
answered Simultaneous maximization of two Generalized Rayleigh Ritz Ratios
Aug
28
answered Semi Definite Relaxation for a Quadratic Feasibility Problem using CVX
Jun
25
awarded  Citizen Patrol
Feb
12
comment Solution Existence of a System of Complex Quadratic Equations
I would like to know the conditions so that there is a solution to the equation system.
Feb
12
revised Solution Existence of a System of Complex Quadratic Equations
added 11 characters in body
Feb
11
comment Solution Existence of a System of Complex Quadratic Equations
Q_{ij} are complex hermitian matrices.
Feb
11
revised Solution Existence of a System of Complex Quadratic Equations
added 85 characters in body
Feb
11
asked Solution Existence of a System of Complex Quadratic Equations
Sep
11
comment Reference Request (semidefinite relaxation)
Ok, I done it. Thank you.
Sep
11
revised Reference Request (semidefinite relaxation)
added 121 characters in body
Sep
10
asked Reference Request (semidefinite relaxation)
May
23
answered Estimating a sum
Dec
16
comment Minimizing ellipsoid over intersection of ellipsoids
Yes, use $\X \approx \lambda_{\text{max}}uu^T$ where $\lambda_{\text{max}}$ is the maximum eigenvalue with u eigenvector. There are other approximations but I barely remenber them...
Dec
15
comment Minimizing ellipsoid over intersection of ellipsoids
Yes: i) Your problem as it is, is non-convex ii) Semidefinite programming relaxation can give you an approximate solution of the problem (since you are dropping the rank-one constraint). iii) There might be the case where ALWAYS the semidefinite relaxation gives a rank-one solution. In that case, the solution to the semidefinite relaxation is the optimal value of your problem. Results about this are derived via studying the dual problem of the semidefinite relaxation.