Efficient Algorithms for a Class of Stochastic Hidden Convex Optimization and Its Applications in Network Revenue Management
针对一类具有隐凸性的随机非凸优化问题，设计了三种高效收敛到全局最优的算法，其中镜像随机梯度法在复杂度上达到最优，并在航空客运和货运网络收益管理中优于现有竞标价格控制策略。
Stochastic Hidden Convex Optimization and Its Applications How to solve nonconvex optimization to global optimality is challenging and important for various applications. In “Efficient Algorithms for a Class of Stochastic Hidden Convex Optimization and Its Applications in Network Revenue Management,” Chen, He, Hu, and Ye designed three algorithms that converge to global optimality efficiently for a class of stochastic nonconvex optimization that admits implicit hidden convexity (there exists an inaccessible convex reformulation). In particular, the complexity of the proposed mirror stochastic gradient (MSG) method matches the optimal complexity of black-box first-order methods for stochastic convex optimization. The authors applied the proposed MSG algorithm to solve both passenger and air-cargo network revenue management problems considering the booking limit control policy. The extensive numerical experiments demonstrate the superior performance of MSG algorithm for booking limit control with higher revenue and lower computation cost than state-of-the-art bid-price-based control policies, especially when the variance of random capacity is large.