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There is nothing more practical than a good theory.

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
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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)
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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.
Dec
15
revised Minimizing ellipsoid over intersection of ellipsoids
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Dec
15
comment Minimizing ellipsoid over intersection of ellipsoids
You should try to define more 'exact results'. From my point of view you might need to consider whether or not the semidifinite relaxation of your problem leads to a rank-one solution of the problem (otherwise, you will just get a lower bound of the solution). See L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Rev., vol. 38, pp. 49–95, 1996." for more info.
Dec
15
answered Minimizing ellipsoid over intersection of ellipsoids
Nov
18
comment minimizing functions over simple matrix inequalities
As a general statement: objective function is convex and constraints are afine---> it can be solved by either interior point methods or grandient methods. On the other hand, your statement: if A is an arbitrary real matrix, the minimization problem above is at least as difficult as solving the matrix equation itself, since it contains that problem, I disagree. Indeed, in the gradient method is used as a projector and the problem it is not solved though.
Nov
11
revised Algorithm for the intersection of a vector subspace with a cone of non-negative vectors
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Nov
11
comment Estimation of X in Gaussian noise
@Igor The problem is about detection, no estimation indeed.