Convex and Stochastic Optimization

This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main algorithms for stochastic programs, while the theoretical aspects are carefully dealt with. The reader is shown how these tools can be applied to various fields, including approximation theory, semidefinite and second-order cone programming and linear decision rules.

This textbook is recommended for students, engineers and researchers who are willing to take a rigorous approach to the mathematics involved in the application of duality theory to optimization with uncertainty.

Provides a pedagogical, self-contained analysis of the theory of convex optimization and stochastic programming Offers a synthetical view of many applications such as semidefinite programming, Markov processes, generalized convexity and optimal transport Includes a study of algorithmic aspects: dynamic programming, stochastic dual dynamic programming (in the case of convex Bellman value functions) and linear decision rules

Auteur

J.F. Bonnans is an expert in convex analysis and dynamic optimization, both in the deterministic and stochastic setting. His main contributions deal with the sensitivity analysis of optimization problems, high order optimality conditions, optimal control and stochastic control. He worked on quantization methods for stochastic programming problems, on the approximate dynamic programming for problems with monotone value function, and on sparse linear regression.

Contenu
1 A convex optimization toolbox.- 2 Semidenite and semiinnite programming.- 3 An integration toolbox.- 4 Risk measures.- 5 Sampling and optimizing.- 6 Dynamic stochastic optimization.- 7 Markov decision processes.- 8 Algorithms.- 9 Generalized convexity and transportation theory.- References.- Index.