Constrained minimization problems, in particular optimal control problems, are considered, where convexity requirements may not be satisfied. Various criteria for existence, or uniqueness, of a minimum are discussed. Criteria for necessary (Karush-Kuhn-Tucker or Pontryagin) conditions to be also sufficient for a minimum are discussed as well. Some of these depend on generalized-convexity properties such as invexity or V-invexity.