The book is devoted to investigation of polynomial optimization problems, including Boolean problems which are the most important part of mathematical programming. It is shown that the methods of nondifferentiable optimization can be used for finding solutions of many classes of polynomial problems and for obtaining good dual estimates for optimal objective value in these problems.
Preface. 1. Elements of Convex Analysis, Linear Algebra, and Graph Theory. 2. Subgradient and epsilon-Subgradient Methods. 3. Subgradient-Type Methods with Space Dilation. 4. Elements of Information and Numerical Complexity of Polynomial Extremal Problems. 5. Decomposition Methods Based on Nonsmooth Optimization. 6. Algorithms for Constructing Optimal on Volume Ellipsoids and Semidefinite Programming. 7. The Role of Ellipsoid Method for Complexity Analysis of Combinatorial Problems. 8. Semidefinite Programming Bounds for Extremal Graph Problems. 9. Global Minimization of Polynomial Functions and 17-th Hilbert Problem. References.