Abstract
Optimization problems in which the variable is not a vector but a symmetric
matrix which is required to be positive semidefinite have been intensely studied
in the last ten years. Part of the reason for the interest stems from the
applicability of such problems to such diverse areas as designing the strongest
column, checking the stability of a differential inclusion, and obtaining tight
bounds for hard combinatorial optimization problems. Part also derives from
great advances in our ability to solve such problems efficiently in theory and in
practice (perhaps ‘or’ would be more appropriate: the most effective computational
methods are not always provably efficient in theory, and vice versa).
Here we describe this class of optimization problems, give a number of examples
demonstrating its significance, outline its duality theory, and discuss
algorithms for solving such problems.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Numerical Analysis
Cited by
317 articles.
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