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

Author:

Chen Xin1ORCID,He Niao2ORCID,Hu Yifan23ORCID,Ye Zikun4ORCID

Affiliation:

1. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;

2. Department of Computer Science, ETH Zürich, 8092 Zürich, Switzerland;

3. College of Management of Technology, EPFL, 1015 Lausanne, Switzerland;

4. Michael G. Foster School of Business, University of Washington, Seattle, Washington 98195

Abstract

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.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

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