Introduction to optimization and semidifferential calculus. (Q2880314)

The book under review is a self-contained textbook for undergraduates on finite-dimensional optimization. It is divided into 5 chapters. The text is completed with numerous examples and exercises.NEWLINENEWLINE The first, introductory chapter contains basic concepts and necessary theoretical background for further material of the book (maxima, minima, supremum, infimum Euclidean space, open, closed and compact sets, continuity of functions).NEWLINENEWLINE The second and third chapters deal with theoretical concepts and theorems, which play a crucial role in optimization theory and optimization algorithms.NEWLINENEWLINE In Chapter 2, some theorems on existence of minimizers are proved and the concept of convexity and its generalizations are introduced. Some properties of the introduced concepts are proved.NEWLINENEWLINE A well-integrated treatment of semidifferential calculus with emphasis on Hadamard subdifferential and its relations to convexity, continuity and Fréchet differentiability is contained in Chapter 3.NEWLINENEWLINE Chapter 4 is devoted to theory and algorithms of optimization. Optimality conditions, admissible directions, primal and dual necessary optimality conditions are studied, methods of solving linear, quadratic, convex and some nonconvex optimization problems with affine equality and inequality constraints are outlined. The next includes also the elements of two-person zero-sum game theory.NEWLINENEWLINE Chapter 5 contains the theory of constrained differentiable optimization. Both unconstrained and constrained differentiable optimization problems are considered. Lagrange multipliers theorem as well as Karush-Kuhn-Tucker theorems are proved.NEWLINENEWLINE The book is completed with two appendices. Appendix A contains the proofs on inverse and implicit function theorems. Appendix B contains results to examples and exercises placed in the end of the particular chapters throughout the book.