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Journal of Convex Analysis 28 (2021), No. 4, [final page numbers not yet available]
Copyright Heldermann Verlag 2021

Optimization of Fitzpatrick Functions and a Numerical Minimization Algorithm

Ivan Raykov
University of Arkansas, Pine Bluff, U.S.A.

M. Zuhair Nashed
University of Central Florida, Orlando, U.S.A.

We consider optimization problems for a class of convex functions on H × H introduced by Simon Fitzpatrick, where H is a real Hilbert space. We show that the minimization problem of Fitzpatrick functions can be transformed from solving of the correspondent differential inclusions (d.i) on H × H, to solving simplified d.i. on H. By using the idea of optimization of Fitzpatrick functions we introduce a numerical algorithm for solving convex smooth optimization problems by reducing the number of the independent variables. We present a comparative study with numerical examples. Finally, we show that Fitzpatrick functions are closely related to Lyapunov functions.

Keywords: Maximal monotone operator, lower semicontinuous convex maps, differential inclusions, optimization problems.

MSC: 46N10, 47N10.

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