Karush-Kuhn-Tucker Proximity Measure for Multi-Objective Optimization Based on Numerical Gradients


A measure for estimating the convergence characteristics of a set of non-dominated points obtained by a multi-objective optimization algorithm was developed recently. The idea of the measure was developed based on the Karush-Kuhn-Tucker (KKT) optimality conditions which require the gradients of objective and constraint functions. In this paper, we extend the scope of the proposed KKT proximity measure by computing gradients numerically and evaluating the accuracy of the numerically computed KKT proximity measure with the same computed using the exact gradient computation. The results are encouraging and open up the possibility of using the proposed KKTPM to non-differentiable problems as well.