Kernel Based Regularized Multiple Criteria Linear Programming Model

Abstract

Although Regularized Multiple Criteria Linear Programming (RMCLP) model has shown its effectiveness in classification problems, its inherent drawback of linear formulation limits itself into only solving linear classification problems. To extend RMCLP into solving non-linear problems, in this paper, we propose a kernel based RMCLP model by using a form $ w = \sum\limits^{N}_{i=1}\beta_{i}\phi(x_{i})$ to replace the original weight w in RMCLP model. Empirical studies on synthetic and real-life datasets demonstrate that our new model is capable to classify non-linear datasets. Moreover, comparisons to SVM and MCQP also exhibit the fact that our new model is superior to other non-linear models in classification problems.