Optimization methods. An introduction (Q5900176)

The author presents a textbook on the theory of mathematical optimization. As usual in this field, he starts with basic tools of convex analysis. So, the reader is familiarized with algebraic and topological properties of convex sets and convex functions. On the base of separation theorems, structural assertions about polyhedral sets, about the solvability of linear inequality systems and about the subdifferential of convex functions are derived. The main part of the book is devoted to necessary and sufficient optimality conditions of first and of second order for optimization problems with inequality and/or equality constraints including the various kinds of constraint qualifications. Some remarks to Lagrange duality complete the text. Finally, the last part contains basic results of linear programming: solvability, duality and simplex method.