For nonconvex optimization problems whose objective is the prediction function of a trained Support Vector Regression (SVR) model with the Gaussian radial basis function (RBF) kernel (RBF-SVR), we present a framework that applies the difference of convex functions (DC) algorithm (DCA) by exploiting the analytical structure of the RBF kernel to construct an explicit DC decomposition. Specifically, we derive in closed form both the lower bound $μ$ of the strong convexity parameter of the DC components and the upper bound $L$ of the gradient Lipschitz constant of the subproblem. Both $μ$ and $L$ are determined solely by the post-training dual-coefficient sum $C_α$ and the RBF kernel parameter $γ$, together with the DC decomposition parameter $ρ$, and they share a common leading term $C_αρ$. Through numerical experiments on six benchmark functions, we show that $C_αρ$ is the primary single quantity characterizing both the convergence properties and the initial-point dependence of DCA, and further demonstrate that it decomposes into two independent pathways, $C \to C_α$ and $γ\to ρ$, with its primary variation governed by the SVR hyperparameters $(C, γ)$. Together, these results allow the convergence properties of DCA on RBF-SVR to be assessed in advance through the single scalar quantity $C_αρ$: approximately from $(C, γ)$ before training, and exactly in closed form after training.

翻译：针对目标函数为经训练的高斯径向基函数（RBF）核支持向量回归（SVR）模型（RBF-SVR）预测函数的非凸优化问题，我们提出一个利用RBF核分析结构构建显式DC（凸函数差）分解，从而应用DC算法（DCA）的框架。具体地，我们推导了DC分量的强凸性参数下界μ与子问题梯度Lipschitz常数上界L的闭式表达式。μ与L完全由训练后对偶系数之和Cα、RBF核参数γ及DC分解参数ρ共同决定，且共享主导项Cαρ。通过在六个基准函数上的数值实验，我们证明Cαρ是同时刻画DCA收敛特性与初始点依赖性的核心单一量，并进一步阐明其分解为两条独立路径（C → Cα和γ→ρ），且主要变化受SVR超参数(C,γ)调控。综合而言，这些结果使得基于RBF-SVR的DCA收敛特性可通过单一标量Cαρ实现预先评估：训练前可依据(C,γ)近似估计，训练后则以闭式精确确定。