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：针对目标函数为训练后高斯径向基函数(RBF)核支持向量回归(RBF-SVR)模型的预测函数这类非凸优化问题，我们提出了一种利用凸函数差分(DC)算法(DCA)的框架，通过发掘RBF核的分析结构来构建显式DC分解。具体而言，我们以闭式形式推导了DC分量的强凸性参数下界$μ$以及子问题梯度Lipschitz常数上界$L$。$μ$和$L$完全由训练后对偶系数之和$C_α$、RBF核参数$γ$以及DC分解参数$ρ$共同决定，且共用主导项$C_αρ$。通过在六个基准函数上的数值实验，我们证明$C_αρ$是同时表征DCA收敛特性和初始点依赖性的主要单一量，并进一步表明它可分解为$C \to C_α$和$γ\to ρ$两条独立路径，其主要变异由SVR超参数$(C, γ$支配。综合这些结果，可通过单一标量$C_αρ$预先评估DCA在RBF-SVR上的收敛特性：在训练前可近似通过$(C, γ)$估算，而在训练后则以闭式形式精确确定。