bio | website | |
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location | Can Pastilla | |
age | ||
visits | member for | 3 years, 10 months |
seen | yesterday | |
stats | profile views | 259 |
There is nothing more practical than a good theory.
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
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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)
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. |
Dec 15 |
revised |
Minimizing ellipsoid over intersection of ellipsoids
added 154 characters in body |
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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