Pardalos, Panos M. An open global optimization problem on the unit sphere. (English) Zbl 0822.90125 J. Glob. Optim. 6, No. 2, 213 (1995). Summary: The author poses the following problem: \[ \text{global max}\quad \Phi_ n(x)= \prod_{1\leq i< j\leq n} \| x_ i- x_ j\|\quad\text{s.t.}\quad \| x_ i\|= 1,\quad i= 1,\dots,n\tag{1} \] and \(x_ i\in \mathbb{R}^ 3\), for all \(i= 1,\dots, n\). The points \(x_ 1,\dots, x_ n\) which give the global maximum of (1) are called the elliptic Fekete points (of order \(n\)). Problem (1) has many local maxima and saddle points. There is no known algorithm for computing an exact (or approximate) global maximum for the above problem. Cited in 2 Documents MSC: 90C30 Nonlinear programming Keywords:elliptic Fekete points PDFBibTeX XMLCite \textit{P. M. Pardalos}, J. Glob. Optim. 6, No. 2, 213 (1995; Zbl 0822.90125) Full Text: DOI References: [1] Michael Shub and Steve Smale (1993), Complexity of Bezout’s Theorem III. Condition Number and Packing,J. of Complexity 9, 4-14. · Zbl 0846.65018 · doi:10.1006/jcom.1993.1002 [2] M. Tsuji (1959),Potential Theory in Modern Function Theory, Maruzen Co., Tokyo. · Zbl 0087.28401 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.