Information Relaxations, Duality, and Convex Stochastic Dynamic Programs (Online Appendix)

Online Appendices for Information Relaxations and Duality in Stochastic Dynamic Programs

Information Relaxations, Duality, and Convex Stochastic Dynamic Programs

We consider the information relaxation approach for calculating performance bounds for stochastic dynamic programs (DPs). This approach generates performance bounds by solving problems with relaxed nonanticipativity constraints and a penalty that punishes violations of these nonanticipativity constraints. In this paper, we study DPs that have a convex structure and consider gradient penalties t...

Lagrangian Primal Dual Algorithms in Online Scheduling

We present a primal-dual approach to design algorithms in online scheduling. Our approach makes use of the Lagrangian weak duality and convexity to derive dual programs for problems which could be formulated as convex assignment problems. The constraints of the duals explicitly indicate the online decisions and naturally lead to competitive algorithms. We illustrate the advantages and the flexi...

Lagrangian Duality based Algorithms in Online Scheduling

We consider Lagrangian duality based approaches to design and analyze algorithms for online energy-efficient scheduling. First, we present a primal-dual framework. Our approach makes use of the Lagrangian weak duality and convexity to derive dual programs for problems which could be formulated as convex assignment problems. The duals have intuitive structures as the ones in linear programming. ...

Information Relaxations and Duality in Stochastic Dynamic Programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a “penalty” that punishes violations of nonanticipativity. In applications, the h...