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Duality of optimization problems with gauge functions. (arXiv:1712.04690v1 [math.OC])
来源于:arXiv
Recently, Yamanaka and Yamashita (2017) proposed the so-called positively
homogeneous optimization problems, which generalize many important problems, in
particular the absolute-value and the gauge optimizations. They presented a
closed dual formulation for these problems, proving weak duality results, and
showing that it is equivalent to the Lagrangian dual under some conditions. In
this work, we focus particularly in optimization problems whose objective
functions and constraints consist of some gauge and linear functions. Through
the positively homogeneous framework, we prove that both weak and strong
duality results hold. We also discuss necessary and sufficient optimality
conditions associated to these problems. Finally, we show that it is possible
to recover primal solutions from Karush-Kuhn-Tucker points of the dual
formulation. 查看全文>>