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Applying the Karush\u2013Kuhn\u2013Tucker (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.<\/jats:p>","DOI":"10.1007\/s11063-025-11780-8","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T11:23:03Z","timestamp":1753183383000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["FLSVR: Solving Lagrangian Support Vector Regression Using Functional Iterative Method"],"prefix":"10.1007","volume":"57","author":[{"given":"Yogendra","family":"Meena","sequence":"first","affiliation":[]},{"given":"P.","family":"Anagha","sequence":"additional","affiliation":[]},{"given":"S.","family":"Balasundaram","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,22]]},"reference":[{"key":"11780_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801389","volume-title":"An introduction to support vector machines and other kernel based learning method","author":"N Cristianini","year":"2000","unstructured":"Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines and other kernel based learning method. 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