Support vector regression with Mean Absolute Percentage Error (MAPE) loss is theoretically well-motivated for forecasting applications where accuracy is evaluated in relative terms, but the sample-dependent dual box constraints it induces have not been addressed in the published SMO literature. We derive a Sequential Minimal Optimization algorithm for this setting and prove a structural-invariance result: the MAPE modification affects exactly two components of the SMO iteration -- working-set selection and analytic-update clipping -- leaving gradient bookkeeping and curvature computation identical to classical epsilon-SVR. Building on this invariance, we establish four efficiency improvements (asymmetric freeze-counters, warm-starting, block working-set updates of size four, and per-pair tolerance scaling) and resolve a previously-open convergence problem for the odd-symmetry kernel variant via adaptive spectral regularization. Numerical validation against three reference solvers across eleven synthetic configurations certifies solution agreement within standard tolerance. Wall-time benchmarks show the present algorithm achieves the lowest median runtime on every tested configuration against OSQP, MOSEK, and Clarabel. At production scale, the algorithm converges on the California Housing benchmark while the patched LIBSVM reference implementation reaches its iteration ceiling without satisfying optimality -- demonstrating the practical necessity of the theoretical efficiency mechanisms. An open-source R package and an explicit solver-adaptation recipe are provided.

翻译：平均绝对百分比误差（MAPE）损失的支持向量回归在相对精度评估的预测应用中具有坚实的理论动机，但其所引发的样本相关对偶盒约束至今未在已发表的SMO文献中得到解决。我们针对该设定推导出一种序列最小优化算法，并证明了一个结构不变性结果：MAPE修改仅影响SMO迭代中的两个组件——工作集选择与解析更新裁剪——而梯度记录与曲率计算则与经典$\varepsilon$-SVR完全相同。基于此不变性，我们提出了四项效率改进（非对称冻结计数器、热启动、大小为四的块工作集更新以及逐对容差缩放），并通过自适应谱正则化解决了奇对称核变体中一个此前未解决的收敛问题。与三个参考求解器在11种合成配置上的数值验证确保了在标准容差范围内解的一致性。墙钟时间对比表明，本算法在OSQP、MOSEK和Clarabel的每个测试配置上都实现了最低中位数运行时间。在生产规模下，本算法在California Housing基准上收敛，而经补丁的LIBSVM参考实现达到迭代上限时仍未满足最优性——这证明了理论效率机制的实际必要性。我们还提供了一个开源R包与显式求解器适配方案。