The Karush-Kuhn-Tucker (KKT) approach is a well established classical method to solve non-linear programming (NLP) optimization problems. The aim of this work is to integrate the KKT method into the Hopfield Neural Networks (HNN) and hence create a new algorithm, the KKT-hopfield neural networks (KHN) for solving nonlinear optimization problems that contain inequality constraints. In this work, the development and the testing of the KHN algorithm was carried out. The KHN algorithm was used for solving two engineering design problems which were; 'optimization of the design of a pressure vessel' (P1) and the 'optimization of the design of a tension/compression spring' (P2). The computational performance of the KHN algorithm was then compared against the modified particle swarm optimization (PSO) algorithm of previous work on similar engineering problems. Comparative studies and analysis were then carried out based on the optimized results. © 2011 Praise Worthy Prize S.r.l. - All rights reserved.