Title: Convex analysis : theory and applications /
Authors: Magaril-Ilʹyaev, G. G. 1944-; Tikhomirov, V. M. 1934-
Publisher: American Mathematical Society,
Year: 2003
Subjects: Convex geometry.; Descrete geometry.; Functional analysis.; Operator theory.; Discrete geometry
Contents: Ch. 1. Theory -- 1. Basic definitions -- 2. Duality in convex analysis -- 3. Convex calculus -- 4. Finite-dimensional convex geometry -- 5. Convex extremal problems -- 6. Supplement: Convex analysis in vector spaces -- Ch. 2. Applications -- 7. Convex analysis of subspaces and cones and the theory of linear equations and inequalities -- 8. Classical inequalities, problems of geometry and mechanics -- 9. Kolmogorov-type inequalities for derivatives -- 10. Convex analysis and extremal problems of approximation and recovery -- Ch. 3. Appendix -- 11. Basic theorems of convex analysis -- 12. Supplementary topics of convex analysis -- 13. Convex analysis and the theory of extremum.