Optimality Conditions: Abnormal and Degenerate Problems

This text is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local integral quadratic form properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed.