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A General Scenario Theory for Nonconvex Optimization and Decision Making.

Authors :
Campi, Marco Claudio
Garatti, Simone
Ramponi, Federico Alessandro
Source :
IEEE Transactions on Automatic Control; Dec2018, Vol. 63 Issue 12, p4067-4078, 12p
Publication Year :
2018

Abstract

The scenario approach is a general methodology for data-driven optimization that has attracted a great deal of attention in the past few years. It prescribes that one collects a record of previous cases (scenarios) from the same setup in which optimization is being conducted and makes a decision that attains optimality for the seen cases. Scenario optimization is by now very well understood forconvexproblems, where a theory exists that rigorously certifies the generalization properties of the solution, that is, the ability of the solution to perform well in connection to new situations. This theory supports the scenario methodology and justifies its use. This paper considersnonconvexproblems. While other contributions in the nonconvex setup already exist, we here take a major departure from previous approaches. We suggest that the generalization level is evaluated only after the solution is found and its complexity in terms of the length of a support subsample (a notion precisely introduced in this paper) is assessed. As a consequence, the generalization level is stochastic and adjusted case by case to the available scenarios. This fact is key to obtain tight results. The approach adopted in this paper applies not only to optimization, but also to generic decision problems where the solution is obtained according to a rule that is not necessarily the optimization of a cost function. Accordingly, in our presentation we adopt a general stance of which optimization is just seen as a particular case. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00189286
Volume :
63
Issue :
12
Database :
Complementary Index
Journal :
IEEE Transactions on Automatic Control
Publication Type :
Periodical
Accession number :
133371865
Full Text :
https://doi.org/10.1109/TAC.2018.2808446