Integration of progressive hedging and dual decomposition in stochastic integer programs

نویسندگان

  • Ge Guo
  • Gabriel Hackebeil
  • Sarah M. Ryan
  • Jean-Paul Watson
  • David L. Woodruff
چکیده

We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. We report computational results on server location and unit commitment instances.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

We present a method for computing lower bounds in the Progressive Hedging Algorithm (PHA) for two-stage and multi-stage stochastic mixedinteger programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated durin...

متن کامل

A Progressive Hedging Based Branch-and-Bound Algorithm for Stochastic Mixed-Integer Programs

Progressive Hedging (PH) is a well-known algorithm for solving multi-stage stochastic convex optimization problems. Most previous extensions of PH for stochastic mixed-integer programs have been implemented without convergence guarantees. In this paper, we present a new framework that shows how PH can be utilized while guaranteeing convergence to globally optimal solutions of stochastic mixed-i...

متن کامل

Combining Progressive Hedging with a Frank-wolfe

We present a new primal-dual algorithm for computing the value of the Lagrangian 6 dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity con7 straints. The algorithm relies on the well-known progressive hedging method, but unlike previous 8 progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal 9 Lagrangian dual value....

متن کامل

On the implementation of a log-barrier progressive hedging method for multistage stochastic programs

A progressive hedging method incorporated with self-concordant barrier functions has been developed by Zhao [23] for solving multistage stochastic programs. The method relaxes the nonanticipativity constraints by the Lagrangian dual approach and smooths the Lagrangian dual function by self-concordant barrier functions. This paper discusses in detail the implementation of this method and reports...

متن کامل

PySP: modeling and solving stochastic programs in Python

Although stochastic programming is a powerful tool for modeling decisionmaking under uncertainty, various impediments have historically prevented its widespread use. One key factor involves the ability of non-specialists to easily express stochastic programming problems as extensions of deterministic models, which are often formulated first. A second key factor relates to the difficulty of solv...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Oper. Res. Lett.

دوره 43  شماره 

صفحات  -

تاریخ انتشار 2015