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Article Citation - WoS: 1Citation - Scopus: 1Spline Based Sparseness and Smoothness for Partially Nonlinear Model Via C-Fused Lasso(American Institute of Mathematical Sciences, 2025) Taylan, P.; Yerlikaya-¨Ozkurt, F.; Tez, M.One of the most beneficial and widely used models for data analysis are partially nonlinear models (PNLRM), which consists of parametric and nonparametric components. Since the model includes the coefficients of both the parametric and nonparametric parts, the complexity of the model will be high and its interpretation will be very difficult. In this study, we propose a procedure that not only achieves sparseness, but also smoothness for PNLRM to obtain a simpler model that better explains the relationship between the response and covariates. Thus, the fused Lasso problem is taken into account where nonparametric components are expressed as a spline basis function, and then the Fused Lasso estimation problem is built and expressed in terms of conic quadratic programming. Applications are conducted to evaluate the performance of the proposed method by considering commonly utilized measures. Promising results are obtained, especially in the data with nonlinearly correlated variables. © (2025), (American Institute of Mathematical Sciences). All rights reserved.Article Citation - WoS: 2A new approach to adaptive spline threshold autoregression by using Tikhonov regularization and continuous optimization(Taru Publications, 2019) Yalaz, S.; Taylan, P.; Ozkurt, F. YerlikayaIn this study adaptive spline threshold autoregression and conic quadratic programming is used to develope conic adaptive spline threshold autoregression. With the introduced approach the second stepwise algorithm of adaptive spline threshold autoregression model turned to the Tikhonov regularization problem which was transformed into conic quadratic programming problem. The aim is to attain an optimum solution chosen in many solutions obtained by determining the bounds of the optimization problem using multiobjective optimization approach. Furthermore, in application part we used two different data set to compare performances of linear regression, adaptive spline threshold autoregression and conic adaptive spline threshold autoregression approaches.
