Directional Derivative for the Value Function in Mathematical Programming
The conditions for the existence of the directional derivative of the optimal value function in mathematical programming is a difficult question still not completely solved. Here we study a case where the directional derivative is obtained with a nice formula when some corresponding optimal solutions have Lipschitzian or Hölderian directional behaviour. These calm properties for optimal solutions are obtained with near to minimal assumptions and regularity conditions (constraints qualification) as illustrated by examples.
KeywordsDirectional Derivative Constraint Qualification Nonlinear Programming Problem Critical Direction Marginal Function
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