Optimization models based on coherent regret measures and coherent risk measures are of essential importance in financial management and reliability engineering . This paper studies the dual representations of these two measures . The relationship between risk envelopes and regret envelopes are established by using the Lagrangian duality theory. The notion of effective scaling domain is introduced and its properties are discussed .
Optimization models based on coherent and averse risk measures are of essential importance in financial management and business operations . 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 . The relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. It is then pointed out that 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 constraints that arises from a reformulation of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms .
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regret measures and coherent
and averse
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reliability engineering
business operations
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studies
begins with a study on
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these two measures
risk and regret measures and their impact on modeling multistage decision making under uncertainty
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are
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The notion of effective scaling domain is introduced and its properties are discussed
It is then pointed out that 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 constraints that arises from a reformulation of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms