Optimization —— A Theory of Necessary Conditions

----- 优化:必要条件理论

ISBN: 9780691616834 出版年：2015 页码：439 Neustadt, Lucien W Princeton University Press

This book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized lagrange multiplier rules are derived for optimization problems with equality and generalized inequality" constraints. The treatment stresses the importance of the choice of the underlying set over which the optimization is to be performed, the delicate balance between differentiability-continuity requirements on the constraint functionals, and the manner in which the underlying set is approximated by a convex set. The generalized multiplier rules are used to derive abstract maximum principles for classes of optimization problems defined in terms of operator equations in a banach space. It is shown that special cases include the usual maximum principles for general optimal control problems described in terms of diverse systems such as ordinary differential equations, functional differential equations, volterra integral equations, and difference equations.