基于量词消去的SAGIN中多层卸载乘积的精确DC表示
Exact DC Representation of Multi-Tier Offloading Product in SAGINs via Quantifier Elimination
AI总结：
针对SAGIN任务卸载的非凸规划问题，通过量词消去得到精确DC表示，结合CCP实现SOCP可解，较SGP提速8.9倍且达近全局解。
AI中文摘要：
空天地一体化网络（SAGIN）中的任务卸载会产生具有三次耦合的非凸符号或多项式规划问题。序列几何规划（SGP）通过指数锥表示对其进行近似，但这超出了CVXPYgen等嵌入式代码生成器的二阶锥规划（SOCP）上限。我们通过量词消去推导了在实数上精确认证的凸差（DC）表示，并应用凸凹过程（CCP），其SOCP子问题为未来的嵌入式代码生成消除了这一结构障碍。与BARON全局求解器的比较显示，SGP和CCP均达到近全局解；CCP还将平均求解时间从SGP的0.1012秒降至0.0113秒，提速8.9倍。
英文摘要：
Task offloading in space--air--ground integrated networks (SAGIN) yields non-convex signomial or polynomial programs with cubic couplings. Sequential geometric programming (SGP) approximates them via exponential cone representations, which exceeds the second-order cone programming (SOCP) ceiling of embedded code generators such as CVXPYgen. We derive a difference-of-convex (DC) representation exactly certified over the reals by quantifier elimination and apply the convex--concave procedure (CCP), whose SOCP subproblems remove this structural obstacle to future embedded code generation. Comparisons with the BARON global solver show that SGP and CCP both attain near-global solutions. CCP further reduces the average solution time from SGP's $0.1012$~s to $0.0113$~s, an $8.9$-fold speedup.
