Constrained Optimization Problems
Mikhail Moklyachuk · 2021
This chapter introduces some definitions of optimality. It formulates a theorem about sufficient conditions for optimality in (not necessarily convex and regular) constrained optimization problems. The theory of sub-differentials can be applied in the study of convex optimization problems. The chapter also formulates more general results, which also cover the case of non-differentiable functions. More convenient regularity conditions can be obtained for problems with convex constraints and linear equality constraints. The direct problem and the dual problem are determined symmetrically with respect to the Lagrange function of the direct problem. The chapter presents a theorem on the connection between the optimization problem and its dual problem.