Necessary Conditions of Optimality for Calculus of Variations Problems with Inequality Constraints

摘要

Necessary Conditions of Optimality (NCO) play an important role in the characterization of and search for solutions of Optimization Problems. They enable us to identify a small set of candidates to local minimizers among the overall set of admissible solutions. However, in constrained optimization problems it may happen that necessary conditions of optimality are merely state a relation between the constraints and do not use the objective function to select candidates to minimizers. To avoid this phenomenon, it is necessary to strengthened the NCO. Here, we overview and describe strengthened forms NCO for calculus of variations with inequality constraints.