Let A be a square matrix. If the mapping Ax^+ is Minty-Browder monotone, then A is positive semidefinite. Is the converse true?

07 July 2016 1 5K Report

x=(x_1,...,x_n)^T, x^+=(max(x_1,0),...,max(x_n,0)), A has n lines and Ax^+ means A multiplied by x^+. Everything is real.

Sándor Zoltán Németh

It seems is not true. Take A=[1 1;0 1], x_1=-3, y_1=-1, x_2=2 and y_2=1. Let me modify the question:

When is Ax^+ Minty-Browder monotone?

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