Paper Info
Title
A Note on the Convexity of $\log \det ( I + KX^{-1} )$ and its Constrained Optimization Representation
Abstract
This note provides another proof for the {\em convexity} ({\em strict convexity}) of $\log \det ( I + KX^{-1} )$ over the positive definite cone for any given positive semidefinite matrix $K \succeq 0$ (positive definite matrix $K \succ 0$) and the {\em strictly convexity} of $\log \det (K + X^{-1})$ over the positive definite cone for any given $K \succeq 0$. Equivalent optimization representation with linear matrix inequalities (LMIs) for the functions $\log \det ( I + KX^{-1} )$ and $\log \det (K + X^{-1})$ are presented. Their optimization representations with LMI constraints can be particularly useful for some related synthetic design problems.
Year
Venue
Field
2015
CoRR
Discrete mathematics,Mathematical optimization,Combinatorics,Convexity,Matrix (mathematics),Positive-definite matrix,Mathematics,Constrained optimization
DocType
Volume
Citations 
Journal
abs/1509.00777
0
PageRank 
References 
Authors
0.34
2
1
Name
Order
Citations
PageRank
Kwang Ki Kevin Kim1133.70