Invited Session Tue.2.MA 144

Tuesday, 13:15 - 14:45 h, Room: MA 144

Cluster 22: Stochastic optimization [...]

Topics in stochastic programming


Chair: Guzin Bayraksan



Tuesday, 13:15 - 13:40 h, Room: MA 144, Talk 1

Johannes O. Royset
Nonparametric estimation using exponential epi-splines

Coauthor: Roger Wets


We develop a flexible framework for nonparametric estimation of probability density functions that systematically
incorporates soft information from human sources
and experiences. The framework results in infinite dimensional stochastic optimization problems that are replaced by finite dimensional approximations based on exponential epi-splines. We show consistency of approximations as the order of the epi-spline grows as well as the sample size tends to infinity. We also discuss asympotics and the implementation of soft information that dramatically improves the quality of the estimates.



Tuesday, 14:15 - 14:40 h, Room: MA 144, Talk 3

Raghu Pasupathy
On interior-point based retrospective approximation methods for solving two-stage stochastic linear programs

Coauthor: Soumyadip Ghosh


We consider two-stage stochastic linear programs, the foundational formulation for optimization under uncertainty. The most general form lets the underlying distributions have infinite support. Approximate solutions to such problems are obtained by the sample average approximation approach of solving the program for a finite sample from the distribution. A recent thread of literature focuses on using interior point methods to efficiently solve two-stage programs for finite support random variables. Our contribution generalizes this
formulation by incorporating it into a retrospective approximation (RA) framework. What results is an implementable
interior-point solution paradigm that can be used to solve general two-stage stochastic linear programs to a desirable accuracy. After discussing some basic convergence properties, we characterize the complexity of the algorithm, leading to guidance on the optimal choice of the RA framework's parameters as a function of the effort expended in solving the sub-problems and the effort expended in solving the
master problem.


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