scholarly journals A Concave Value Function Extension for the Dynamic Programming Approach to Revenue Management in Attended Home Delivery

2019 ◽  
Author(s):  
Denis Lebedev ◽  
Paul Goulart ◽  
Kostas Margellos
Keyword(s):  
Dynamic Programming ◽  
Revenue Management ◽  
Value Function ◽  
Home Delivery ◽  
Programming Approach ◽  
Dynamic Programming Approach ◽  
Function Extension

NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 08 (02) ◽  
pp. 231-272 ◽  
Author(s):  
M. FALCONE
Keyword(s):  
Dynamic Programming ◽  
Numerical Methods ◽  
Differential Games ◽  
Value Function ◽  
Approximation Schemes ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Feedback Controls ◽  
Dynamic Programming Approach ◽  
Discrete Time Dynamical System

In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games.

Sign in / Sign up

Export Citation Format

Share Document