Invited Session Tue.1.MA 141

Tuesday, 10:30 - 12:00 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Methods of risk-averse optimization


Chair: Andrzej Ruszczynski



Tuesday, 10:30 - 10:55 h, Room: MA 141, Talk 1

Csaba I. Fabian
Computational aspects of risk-averse optimization


We deal with solution methods for two-stage stochastic linear programming problems, with an emphasis on variants that include convex risk measures. We consider cutting-plane and bundle-type methods. The aim is to specialize general linear programming computing techniques to these stochastic problems; and on the other hand, to work out LP computational techniques based on ideas originally developed for the handling of risk measures.



Tuesday, 11:00 - 11:25 h, Room: MA 141, Talk 2

Andrzej Ruszczynski
Methods for solving risk-averse dynamic optimization problems

Coauthor: Ozlem Cavus


For risk-averse dynamic optimization problems with Markov risk measures, we present several computational methods for finding optimal policies. In particular, we extend to the risk-averse case the value iteration, policy iteration, and mathematical programming approaches. We illustrate the results on several applied problems.



Tuesday, 11:30 - 11:55 h, Room: MA 141, Talk 3

Darinka Dentcheva
Decomposition methods for solving two-stage optimization problems with stochastic ordering constraints

Coauthors: Gabriela Martinez, Eli Wolfhagen


We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. We consider the usual stochastic order,
the increasing convex order, and the multivariate stochastic dominance. We propose decomposition methods to solve the problems and prove their convergence. Additionally, new characterizations of the increasing convex order relation are provided. Our methods exploit the decomposition structure of the risk-neutral two-stage problems and construct successive approximations of the stochastic ordering constraints. Numerical results confirm the efficiency of the methods.


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