|Optimization and Convexity of log det(I+KX-1)
Kwang-Ki K. Kim
International Journal of Control, Automation, and Systems, vol. 17, no. 4, pp.1067-1070, 2019
Abstract : "This paper provides another proof for the convexity (strict convexity) of log det(I +KX1) over the
positive definite cone for any given positive semidefinite matrix K ⪰ 0 (positive definite matrix K ≻ 0) and the
strict convexity of log det(K +X1) over the positive definite cone for any given K ⪰ 0. Equivalent optimization
representations with linear matrix inequalities (LMIs) for the functions log det(I+KX1) and log det(K+X1) are
also presented. It was shown that these optimization representations with LMI constraints can be particularly useful
for some related synthetic design problems. An iterative procedure based on the proposed LMI is presented to solve
the minimax mutual information game with covariance and expected power constraints."
"Coding theory, convex optimization, log-det function, matrix differential, minimax mutual information game, positive definite matrix."