论文信息 - On the rank minimization problem over a positive semidefinite linear matrix inequality

On the rank minimization problem over a positive semidefinite linear matrix inequality

We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidefinite. Our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice. This problem is of importance in many contexts, for example in feedback synthesis problems, and such an example is also provided.

G. Papavassilopoulos | M. Mesbahi

[1] S. Kakutani. A generalization of Brouwer’s fixed point theorem , 1941 .

[2] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[3] K. Goh,et al. Control system synthesis via bilinear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[4] Stephen P. Boyd,et al. Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[5] Farid Alizadeh,et al. Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization , 1995, SIAM J. Optim..

[6] Mehran Mesbahi,et al. A cone programming approach to the bilinear matrix inequality problem and its geometry , 1997, Math. Program..

[7] M. Mesbahi,et al. Solving a class of rank minimization problems via semi-definite programs, with applications to the fixed order output feedback synthesis , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).