173. An interior point approach for multi horizon risk averse stochastic optimization.
Invited abstract in session WC-11: Interior point methods and applications - Part II, stream Interior point methods and applications.
Wednesday, 14:00-16:00Room: B100/5017
Authors (first author is the speaker)
| 1. | Jordi Castro
|
| Dept. of Statistics and Operations Research, Universitat Politecnica de Catalunya | |
| 2. | Laureano F. Escudero
|
| Estadística e Investigación Operativa, Universidad Rey Juan Carlos | |
| 3. | Juan Francisco Monge
|
| Centro de Investigación Operativa, Universidad Miguel Hernández |
Abstract
In a previous paper, the authors presented a novel approach based on a
specialized interior-point method (IPM) for solving large-scale multistage
continuous stochastic optimization problems. This approach considered both
strategic (long-term) and operational (short-term) uncertainties and
decisions.
This work extends the previous approach by incorporating risk-averse
constraints: either expected conditional value-at-risk or expected
conditional stochastic dominance. As in the earlier risk-neutral approach, the
new risk-averse model is reformulated using splitting variables. The
reformulated model remains compatible with the specialized IPM, which computes
the Newton direction by combining Cholesky factorizations with preconditioned
conjugate gradients (PCG).
It is shown that the new reformulated risk-averse constraints simply extend
the preconditioner of the PCG with an additional diagonal matrix, preserving
the efficient solution of systems using the preconditioner.
Preliminary results are reported for the solution of real-world problems
involving several million variables and constraints.
Keywords
- Large-scale optimization
- Stochastic optimization
Status: accepted
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