### PhD Thesis Final Defense to be held on July 11, 2018 at 11:00

*Moraitis Thesis Image*

**Thesis Title***:* Τhe Sign recurrent neural network for unconstrained minimization.

**The examination is open to anyone who wishes to attend (Room 2.2.29, Old ECE Building).**

**Abstract**

In this Thesis, the sign dynamical system for unconstrained minimization of a continuously differentiable function f is examined. This dynamical system has a discontinuous right hand side and, in this Thesis, it is interpreted here as a reccurent neural network which we name the Sign Neural Network. By using Filippov’s approach, we first prove asymptotic convergence of the Sign Neural Network. Also, finite-time convergence of the solutions is established and an improved upper bound for convergence time is given.

A first contribution of this Thesis is a detailed calculation of Filippov’s set-valued map for the Sign Neural Network in the general case, i.e. without any restrictive assumptions on the function f to be minimized. Convergence of the solutions to stationary points of f follows by using standard results, i.e. a generalized version of LaSalle’s invariance principle. Next, in order to prove finite-time convergence of solutions, the applicability of standard results is extended so that they can be applied to the Sign Neural Network. Finally, while establishing finite-time convergence, a novel proving procedure is introduced which (i) allows for milder assumptions to be made on the function f , and (ii) results in an improved upper bound for the convergence time.

Numerical experiments confirm both the effectiveness and finite-time convergence of the Sign Neural Network.

**Supervisor**: Maratos Nicholas, Professor

**PhD student**: Moraitis M.