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Conjugate quasiconvex nonnegative functions. (English) Zbl 0840.90120
Summary: A conjugacy operation defined on the complete lattice \(Q(X)\) of all nonnegative quasiconvex lower semicontinuous functions defined on locally convex space \(X\) and vanishing at zero is considered. Properties of this operation and of the lattice \(Q(X)\) are outlined. In particular, a set of extreme rays of \(Q(X)\) which generates this conic lattice by means of the operation ‘sup’ is described, the connection between summation and the conjugacy operation is established.

MSC:
90C30 Nonlinear programming
49J52 Nonsmooth analysis
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