Convex Analysis and Variational Problems

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Preface to the classics edition; Preface; Part I. Fundamentals of Convex Analysis. I. Convex functions; 2. Minimization of convex functions and variational inequalities; 3. Duality in convex optimization; Part II. Duality and Convex Variational Problems. 4. Applications of duality to the calculus of variations (I); 5. Applications of duality to the calculus of variations (II); 6. Duality by the minimax theorem; 7. Other applications of duality; Part III. Relaxation and Non-Convex Variational Problems. 8. Existence of solutions for variational problems;9. Relaxation of non-convex variational problems (I); 10. Relaxation of non-convex variational problems (II); Appendix I. An a priori estimate in non-convex programming; Appendix II. Non-convex optimization problems depending on a parameter; Comments; Bibliography; Index.

Contains developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). Also includes the theory of convex duality applied to PDEs no other reference presents this in a systematic way