Second-order conditions for existence of augmented Lagrange multipliers for eigenvalue composite optimization problems

2015 ◽  
Vol 63 (1) ◽  
pp. 77-97 ◽  
Author(s):  
Chao Kan ◽  
Wen Song
Keyword(s):  
Lagrange Multipliers ◽  
Optimization Problems ◽  
Second Order ◽  
Order Conditions ◽  
Composite Optimization ◽  
Second Order Conditions

Second-Order Conditions

2018 ◽  
Author(s):  
John E. Prussing
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Conjugate Point ◽  
Test Procedure ◽  
Second Order ◽  
Order Conditions ◽  
Second Order Conditions ◽  
The First Variation ◽  
The Cost ◽  
The Second Variation

Second-order conditions for both parameter optimization problems and optimal control problems are analysed. A new conjugate point test procedure is discussed and illustrated. For an optimal control problem we will examine the second variation of the cost. The first variation subject to constraints provides first-order NC for a minimum of J. Second-order conditions provide SC a minimum.

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