Volume 2002
http://edoc.hu-berlin.de/18452/359
2023-02-06T03:05:31ZLearning algorithms for separable approximations of stochastic optimization problems
http://edoc.hu-berlin.de/18452/8934
Learning algorithms for separable approximations of stochastic optimization problems
Powell, Warren; Ruszczynski, Andrzej; Topaloglu, Huseyin
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
We propose the use of sequences of separable, piecewise linear approximations for solving classes of nondiffferential stochastic optimization problems. The approximations are estimated adaptively using a combination of stochastic gradient information and possibly sample information on the objective function itself. We prove the convergence of several versions of such methods when the objective function is separable and illustrate their behavior on numerical examples. We then demonstrate the preformance on nonseparable problems that arise in the context of two-stage stochastic programming problems, and demonstrate that these techniques provide near optimal solutions with a very fast rate of convergence compared to other solution techniques.
2002-11-05T00:00:00ZA branch-and-price algorithm for multi-stage stochastic integer programming with application to stochastic batch-sizing problems
http://edoc.hu-berlin.de/18452/8933
A branch-and-price algorithm for multi-stage stochastic integer programming with application to stochastic batch-sizing problems
Lulli, Guglielmo; Sen, Suvrajeet
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
In this paper we present a branch-and-price method to solve special structured multi-stage stochastic integer programming problems. We validate our method on two different versions of a multi-stage stochastic batch-sizing problem. One version adopts a recourse formulation, and the other is based on probabilistic constraints. Our algorithmic approach is applicable to both formulations. Our computational results suggest that both classes of problems can be solved using relatively few nodes of a branch-and-price tree. The success of our approach calls for extensions in methodology as well as applications.
2002-10-24T00:00:00ZFrontiers of stochastically nondominated portfolios
http://edoc.hu-berlin.de/18452/8932
Frontiers of stochastically nondominated portfolios
Ruszczynski, Andrzej; Vanderbei, Robert J.
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose mean-risk models which are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of second-order stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean-risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations.
2002-10-24T00:00:00ZRisk aversion via excess probabilities in stochastic programs with mixed-integer recourse
http://edoc.hu-berlin.de/18452/8931
Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse
Schultz, Rüdiger; Tiedemann, Stephan
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
We consider linear two-stage stochastic programs with mixed-integer recourse. Instead of basing the selection of an optimal first-stage solution on expected costs alone, we include into the objective a risk term reflecting the probability that a preselected cost threshold is exceeded. After we have put the resulting mean-risk model into perspective with stochastic dominance, we study further structural properties of the model and derive some basic stability results. In the algorithmic part of the paper, we propose a scenario decomposition method and report initial computational experience.
2002-08-16T00:00:00Z