Necessary First-Order and Second-Order Optimality Conditions in Discrete-Time Stochastic Systems

2019 ◽  
Vol 182 (3) ◽  
pp. 1001-1018
Author(s):  
Nazim I. Mahmudov
Keyword(s):  
Optimality Conditions ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Second Order ◽  
First Order ◽  
Second Order Optimality Conditions

scholarly journals Notes on Constraint Qualifications for Second-Order Optimality Conditions

2019 ◽  
Vol 11 (5) ◽  
pp. 16
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Second Order ◽  
Necessary Optimality Condition ◽  
First Order ◽  
Second Order Optimality Conditions ◽  
Order Constraint ◽  
Local Approximations ◽  
Abadie Constraint Qualification

In the first part of this paper we point out some basic properties of the critical cones used in second-order optimality conditions and give a simple proof of a strong second-order necessary optimality condition by assuming a “modified” first-order Abadie constraint qualification. In the second part we give some insights on second-order constraint qualifications related to second-order local approximations of the feasible set.

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