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Journal of Convex Analysis 12 (2005), No. 1, 081--093
Copyright Heldermann Verlag 2005

Relating U-Lagrangians to Second-Order Epi-Derivatives and Proximal Tracks

Robert Mifflin
Dept. of Mathematics, Washington State University, Pullman, WA 99164-3113, U.S.A.

Claudia Sagastizabal
IMPA, Estrada Doņa Castorina 110, Jardim Botanico, Rio de Janeiro, RJ 22460-320, Brazil

We make use of VU-space decomposition theory to connect three minimization-oriented objects. These objects are U-Lagrangians obtained from minimizing a function over V-space, proximal points depending on minimization over Rn = U + V, and epi-derivatives determined by lower limits associated with epigraphs. We relate second-order epi-derivatives of a function to the Hessian of its associated U -Lagrangian. We also show that the function's proximal points are on a trajectory determined by certain V-space minimizers.

Keywords: U-Lagrangian, proximal point, second-order epi-derivatives.

MSC: 90C31, 49J52, 65K10; 49J53

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