FLSVR: Solving Lagrangian Support Vector Regression Using Functional Iterative Method

• Published in: Neural processing letters Vol. 57; no. 4; p. 71
• Main Authors: Meena, Yogendra, Anagha, P., Balasundaram, S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 22.07.2025; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Classification; Complex Systems; Computational Intelligence; Computer Science; Fixed points (mathematics); Iterative methods; Optimization; Outdoor air quality; Quadratic programming; Regression; Support vector machines; Regression; Kernel methods; Fixed point problem; Quadratic programming problem; Functional iterative method
• ISSN: 1573-773X; 1370-4621; 1573-773X
• DOI: 10.1007/s11063-025-11780-8

The Lagrangian dual of the 2-norm support vector regression (LSVR) solves a quadratic programming problem (QPP) in 2m variables subject to the non-negative variable conditions where m is the size of the training set. Applying the Karush–Kuhn–Tucker (KKT) necessary and sufficient optimality conditions, this work's novel problem formulation is only derived as a fixed point problem in m variables. This problem is solvable either in its original form, having the non-smooth "plus" function, or by considering its equivalent absolute value equation problem using functional iterative methods. A linear convergence rate of the proposed iterative methods is rigorously established under appropriate assumptions. It leads to the unique optimum solution. Numerical experiments performed on several synthetic and real-world benchmark datasets demonstrate that the proposed formulation solved by iterative methods shows similar or better generalization capability with a learning speed much faster than support vector regression (SVR), very close to least squares SVR (LS-SVR), and comparable with ULSVR which indicates its effectiveness and superiority.