Shadow Prices, Duality and Green's Formula for a Class of Optimal Control Problems.

Abstract

A class of optimal control problems is considered in which the cost functional is locally Lipschitz (not necessarily convex or differentiable) and the dynamics linear and/or convex. By using generalized gradients and duality methods of functional analysis, necessary conditions are obtained in which the dual variables admit interpretation as shadow prices (or rates of change of the value function). Applications are presented in three settings: infinite horizon optimal control, optimal control of partial differential equations, and a variational problem with unilateral state constraints. A theorem is proved which characterizes the generalized gradients of integral functionals on L(p). (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1978
Accession Number
ADA064001

Entities

People

  • F. H. Clarke
  • J. P. Aubin

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Computer Programming
  • Differential Equations
  • Dynamics
  • Equations
  • Functional Analysis
  • Integrals
  • Mathematical Analysis
  • Mathematical Programming
  • Mathematics
  • Military Research
  • North Carolina
  • Operations Research
  • Partial Differential Equations
  • Sensitivity
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research