ON LIPSCHITZ FUNCTIONS AND OPTIMIZATION IN HILBERT SPACES

LIPSCHITZ FUNCTIONS AND OPTIMIZATION

Authors

  • benard okelo JOOUST

Keywords:

Lipschitz function, Optimization, Hilbert space

Abstract

Optimization problems have attracted the attention of many mathematicians and researchers over a long period of time. In this work, we consider with the classical results on optimization of functions in infinite-dimensional real Hilbert spaces. In particular, we consider Lipschitz functions. The methodology involves the use of convex optimization techniques. The results show that a Lipschitz function f has a first order optimality condition. Moreover, if f is differentiable at a point x* in Rn and if x* is a local minimum of f, then the del of f(x*) = 0. A simple application involving the Dirichlet problem is also given.  In conclusion, we give the applications of this work to Portfolio Optimization, particularly, stochastic optimization with consideration to Hamilton-Jacobi-Bellman Equation in Hilbert spaces.

Published

21-03-2022

How to Cite

okelo, benard (2022) “ON LIPSCHITZ FUNCTIONS AND OPTIMIZATION IN HILBERT SPACES: LIPSCHITZ FUNCTIONS AND OPTIMIZATION ”, Egerton University International Conference. Available at: https://conferences.egerton.ac.ke/index.php/euc/article/view/218 (Accessed: 4 February 2023).

Issue

Section

Health Systems, Science and Technology