Interval-based KKT framework for support vector machines and beyond


Younus A., Rimsha R., Tunç C.

Journal of Taibah University for Science, vol.18, no.1, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1080/16583655.2024.2334017
  • Journal Name: Journal of Taibah University for Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Keywords: 90C30, 90C46, 90C70, Fritz John conditions, gH -differentiability, interval optimization, Interval-valued functions, KKT conditions, support vector machines
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush–Kuhn–Tucker (KKT) conditions and expands Gordan's theorems for interval linear inequality systems. By applying Gordan's theorem, we can determine the best outcomes for interval optimization problems (IOPs) that have constraints, such as Fritz John and KKT conditions. The optimality conditions are observed with inclusion relations rather than equality. We can use the KKT condition for binary classification with interval data and support vector machines(SVMs). We present some examples to illustrate our results.