Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Risk Minimization, Regret Minimization and Progressive Hedging
  Algorithms   This paper begins with a study on the dual representations of risk and regret
measures and their impact on modeling multistage decision making under
uncertainty. A relationship between risk envelopes and regret envelopes is
established by using the Lagrangian duality theory. Such a relationship opens a
door to a decomposition scheme, called progressive hedging, for solving
multistage risk minimization and regret minimization problems. In particular,
the classical progressive hedging algorithm is modified in order to handle a
new class of linkage constraints that arises from reformulations and other
applications of risk and regret minimization problems. Numerical results are
provided to show the efficiency of the progressive hedging algorithms.

36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom