Journal of Applied Analysis 02 (1996), No. 1, 013--039
Copyright Heldermann Verlag 1996
Epi/Hypo-Convergence: the Slice Topology and Saddle Points Approximation
Adib Bagh
Dept. of Mathematics, University of California, Davis, CA 95616, U.S.A.
We show that the slice convergence of the convex parents of saddle functions implies the epi/hypo-convergence of these saddle functions and hence the convergence of their saddle points. We also obtain conditions for the slice convergence of sums of convex functions. We then apply these results to problems in convex programming, optimal control and Chebyshev approximations.
Keywords: Slice topology, epi/hypo-convergence, saddle points, convex programming, optimal control, Chebyshev approximation.
MSC: 49R99, 90C25, 54B20
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