| Popis: |
For solving minmax location problems in Hilbert spaces Hi, i = 1, …, n, numerically by proximal methods we present in this chapter first a general formula of the projection onto the epigraph of the function h : H1 × … × Hn → ℝ, defined by \( h\left( {x_{1} , \ldots ,x_{n} } \right)\text{: = }\sum\limits_{i = 1}^{n} {\left. {w_{i} } \right\|} \left. {x_{i} } \right\|_{{H_{i} }}^{{\beta_{i} }} \). We consider the situations when βi = 1, i = 1, …, n, and wi = 1, βi = 2, i = 1, …, n, where the formulae given for instance in [3, 33, 34] turn out to be special cases for n = 1 of our considerations. |
