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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Two-stage Stochastic Programming with Linearly Bi-
parameterized Quadratic Recourse - Jong Shi Pang (
University of Southern California)
DTSTART;TZID=Europe/London:20190319T154500
DTEND;TZID=Europe/London:20190319T163000
UID:TALK121276AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/121276
DESCRIPTION:This paper studies the class of two-stage stochast
ic programs (SP) with a linearly bi-parameterized
recourse function defined by a convex quadratic pr
ogram. A distinguishing feature of this new class
of stochastic programs is that the objective funct
ion in the second stage is linearly parameterized
by the first-stage decision variable\, in addition
to the standard linear parameterization in the co
nstraints. Inspired by a recent result that establ
ishes the difference-of-convexity (dc) property of
such a recourse function\, we analyze the almost-
sure subsequential convergence of a successive sam
ple average approximation (SAA) approach combined
with the difference-of-convex algorithm (DCA) for
computing a directional derivative based stationar
y solution of the overall non- convex stochastic p
rogram. Under a basic setup\, the analysis is divi
ded into two main cases: one\, the problem admits
an explicit\, computationally viable dc decomposit
ion with a differentiable con- cave component\, ba
sed on which the discretized convex subproblems to
be solved iteratively can be readily defined\; an
d two\, an implicit bivariate convex-concave prope
rty can be identified via a certain smoothing of t
he recourse function. The first case includes a st
rictly convex second-stage objective and a few spe
cial instances where the second-stage recourse is
convex but not strictly convex. A general convex s
econd-stage recourse function belongs to the secon
d main case\; this case requires the introduction
of the notion of a generalized critical point to w
hich the almost-sure subsequential convergence of
the combined SAA and DCA is established. Overall\,
this research provides the first step in the inve
stigation of this class of two-stage SPs that seem
ingly has not been\, until now\, the object of a f
ocused study in the vast literature of computation
al two-stage stochastic programming.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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