凸確率最適化：動的計画法と離散時間における二重性 Convex Stochastic Optimization : Dynamic Programming and Duality in Discrete Time

著者名：Pennanen, Teemu/Perkkiö, Ari-Pekka

Springer（2024/12/18発売）

• 言語：ENG
• ISBN：9783031764318
• eISBN：9783031764325

Description

This book studies a general class of convex stochastic optimization (CSO) problems that unifies many common problem formulations from operations research, financial mathematics and stochastic optimal control. We extend the theory of dynamic programming and convex duality to allow for a unified and simplified treatment of various special problem classes found in the literature. The extensions allow also for significant generalizations to existing problem formulations. Both dynamic programming and duality have played crucial roles in the development of various optimality conditions and numerical techniques for the solution of convex stochastic optimization problems.

Table of Contents

- 1. Convex Stochastic Optimization.- 2. Dynamic Programming.- 3. Duality.- 4. Absence of a Duality Gap.- 5. Existence of Dual Solutions.