Matrix Inequalities: A Symbolic Procedure to Determine Convexity Automatically

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Matrix-J-unitary Non-commutative Rational Formal Power Series (2004, unknown): “, matrix-positivity of non-commutative polynomials (non-commutative Positivstellensatz) [29, 40, 31, 32], matrix-positivity of FPS kernels [34], matrix-convexity [21, 30].”
POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION (2006, methodology): “with polynomials p in two classes of variables p(a,x) where we shall be interested in matrix convexity in x over ranges of the variable a. Describing this setup fully takes a while, as one can see in [CHSY03] where it is worked out. An engineer might look at [CHSprept], especially the ﬁrst part whic”
NONCOMMUTATIVE CONVEXITY ARISES FROM LINEAR MATRIX INEQUALITIES. (2006, methodology): “(3) Also an algorithm given in [9] and implemented in NCAlgebra determines if a given NC rational function is or is not matrix convex near 0.”
Singularities of rational functions and minimal factorizations: The noncommutative and the commutative setting (2009, background): “Most optimization problems of system theory and control are dimensionless in the sense that the natural variables are matrices of an arbitrary size, and their domain is described by size-independent polynomial or rational inequalities (see [15,29,30]).”