Exact DC Representation of Multi-Tier Offloading Product in SAGINs via Quantifier Elimination

2026/08/06 by Minh-Tuong Nguyen, Vo Phi Son, Dinh Thai Hoang
Engineering · #eess.SP

paper · pdf

arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

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.

Citations

• A new method for reducing algebraic programs to polynomial programs
• Exponential Conic Relaxations for Signomial Geometric Programming
• Joint Offloading and Resource Allocation for Hybrid Cloud and Edge Computing in SAGINs: A Decision Assisted Hybrid Action Space Deep Reinforcement Learning Approach
• Joint Offloading and Resource Allocation for Hybrid Cloud and Edge Computing in SAGINs: A Decision Assisted Hybrid Action Space Deep Reinforcement Learning Approach
• Embedded Code Generation with CVXPY
• Joint Pilot Design and Uplink Power Allocation in Multi-Cell Massive MIMO Systems
• General Heuristics for Nonconvex Quadratically Constrained Quadratic Programming
• DC Decomposition of Nonconvex Polynomials with Algebraic Techniques
• Convex optimization
• Real quantifier elimination is doubly exponential