On the Dual Approach to Recursive Optimization

Matthias Messner, Nicola Pavoni and Christopher Sleet

No 423, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

Abstract: We bring together the theories of duality and dynamic programming. We show that the dual of an additively separable dynamic optimization problem can be recursively decomposed using summaries of past Lagrange multipliers as state variables. Analogous to the Bellman decomposition of the primal problem, we prove equality of values and solution sets for recursive and sequential dual problems. In nonadditively separable settings, the equivalence of the recursive and sequential dual is not guaranteed. We relate recursive dual and recursive primal problems. If the Lagrangian associated with a constrained optimization problem admits a saddle then, even in nonadditively separable settings, the values of the recursive dual and recursive primal problems are equal. Additionally, the recursive dual method delivers necessary conditions for a primal optimum. If the problem is strictly concave, the recursive dual method delivers necessary and sufficient conditions for a primal optimum. When a saddle exists, states on the optimal dual path are subdifferentials of the primal value function evaluated at states on the optimal primal path and vice versa.

Date: 2011
New Economics Papers: this item is included in nep-dge and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://repec.unibocconi.it/igier/igi/wp/2011/423.pdf (application/pdf)

Related works:
Working Paper: On the Dual Approach to Recursive Optimization (2011)
Working Paper: On the Dual Approach to Recursive Optimization
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:igi:igierp:423

Ordering information: This working paper can be ordered from
https://repec.unibocconi.it/igier/igi/

Access Statistics for this paper

More papers in Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University via Rontgen, 1 - 20136 Milano (Italy).
Bibliographic data for series maintained by ().