Global escape strategies for maximizing quadratic forms over a simplex (Q1368742)

The problem of maximizing a quadratic form over the standard simplex is considered, i.e. \(x'\cdot A\cdot x\to \max\), subject to \(x\in\Delta^n\), where \(A\) is a symmetric \(n\times n\) matrix and \(\Delta^n\) is the standard \((n-1)\)-dimensional simplex in \(\mathbb{R}^n\). For this problem an algorithm is obtained, which tries to exploit favorable data constellations in a systematic way, avoiding worst-case behavior. Numerical tests are given.