skip to content

Two-stage Stochastic Programming with Linearly Bi-parameterized Quadratic Recourse

Presented by: 
Jong Shi Pang
Tuesday 19th March 2019 - 15:45 to 16:30
INI Seminar Room 1
This paper studies the class of two-stage stochastic programs (SP) with a linearly bi-parameterized recourse function defined by a convex quadratic program. A distinguishing feature of this new class of stochastic programs is that the objective function in the second stage is linearly parameterized by the first-stage decision variable, in addition to the standard linear parameterization in the constraints. Inspired by a recent result that establishes the difference-of-convexity (dc) property of such a recourse function, we analyze the almost-sure subsequential convergence of a successive sample average approximation (SAA) approach combined with the difference-of-convex algorithm (DCA) for computing a directional derivative based stationary solution of the overall non- convex stochastic program. Under a basic setup, the analysis is divided into two main cases: one, the problem admits an explicit, computationally viable dc decomposition with a differentiable con- cave component, based on which the discretized convex subproblems to be solved iteratively can be readily defined; and two, an implicit bivariate convex-concave property can be identified via a certain smoothing of the recourse function. The first case includes a strictly convex second-stage objective and a few special instances where the second-stage recourse is convex but not strictly convex. A general convex second-stage recourse function belongs to the second main case; this case requires the introduction of the notion of a generalized critical point to which the almost-sure subsequential convergence of the combined SAA and DCA is established. Overall, this research provides the first step in the investigation of this class of two-stage SPs that seemingly has not been, until now, the object of a focused study in the vast literature of computational two-stage stochastic programming.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons