Efficient Algorithms for a Class of Stochastic Hidden Convex Optimization and Its Applications in Network Revenue Management

Xin Chen (), Niao He (), Yifan Hu () and Zikun Ye ()
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Xin Chen: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Niao He: Department of Computer Science, ETH Zürich, 8092 Zürich, Switzerland
Yifan Hu: Department of Computer Science, ETH Zürich, 8092 Zürich, Switzerland; and College of Management of Technology, EPFL, 1015 Lausanne, Switzerland
Zikun Ye: Michael G. Foster School of Business, University of Washington, Seattle, Washington 98195

Operations Research, 2025, vol. 73, issue 2, 704-719

Abstract: We study a class of stochastic nonconvex optimization in the form of min x ∈ X F ( x ) ≔ E ξ [ f ( ϕ ( x , ξ ) ) ] , that is, F is a composition of a convex function f and a random function ϕ . Leveraging an (implicit) convex reformulation via a variable transformation u = E [ ϕ ( x , ξ ) ] , we develop stochastic gradient-based algorithms and establish their sample and gradient complexities for achieving an ϵ -global optimal solution. Interestingly, our proposed Mirror Stochastic Gradient (MSG) method operates only in the original x -space using gradient estimators of the original nonconvex objective F and achieves O ˜ ( ϵ − 2 ) complexities, matching the lower bounds for solving stochastic convex optimization problems. Under booking limits control, we formulate the air-cargo network revenue management (NRM) problem with random two-dimensional capacity, random consumption, and routing flexibility as a special case of the stochastic nonconvex optimization, where the random function ϕ ( x , ξ ) = x ∧ ξ , that is, the random demand ξ truncates the booking limit decision x . Extensive numerical experiments demonstrate the superior performance of our proposed 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.

Keywords: Market; Analytics; and; Revenue; Management; stochastic nonconvex optimization; hidden convexity; gradient methods; passenger network revenue management; air-cargo network revenue management (search for similar items in EconPapers)
Date: 2025
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