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We study a class of stochastic nonconvex optimization in the form of$\min_{x\in\mathcal{X}} F(x):=\mathbb{E}_\xi [f(\phi(x,\xi))]$, i.e., $F$ is acomposition of a convex function $f$ and a random function $\phi$. Leveragingan (implicit) convex reformulation via a variable transformation$u=\mathbb{E}[\phi(x,\xi)]$, we develop stochastic gradient-based algorithmsand establish their sample and gradient complexities for achieving an$\epsilon$-global optimal solution. Interestingly, our proposed MirrorStochastic Gradient (MSG) method operates only in the original $x$-space usinggradient estimators of the original nonconvex objective $F$ and achieves$\tilde{\mathcal{O}}(\epsilon^{-2})$ complexities, which matches the lowerbounds for solving stochastic convex optimization problems. Under bookinglimits control, we formulate the air-cargo network revenue management (NRM)problem with random two-dimensional capacity, random consumption, and routingflexibility as a special case of the stochastic nonconvex optimization, wherethe random function $\phi(x,\xi)=x\wedge\xi$, i.e., the random demand $\xi$truncates the booking limit decision $x$. Extensive numerical experimentsdemonstrate the superior performance of our proposed MSG algorithm for bookinglimit control with higher revenue and lower computation cost thanstate-of-the-art bid-price-based control policies, especially when the varianceof random capacity is large.  KEYWORDS: stochastic nonconvex optimization, hidden convexity, gradientmethods, passenger network revenue management, air-cargo network revenuemanagement

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